How to know the associated integration_UUID's for Integration Objects?

You can see the UUID of the object in the package if you export the object. It doesn't look like you can see it natively in the Appian Designer.

Thanks for your response. Can you please elaborate the point.
In objects tab if we select the integration object, we don't have a export option.
Could you please share the details of how to export all the integration objects and how to know the integration_uuid.
if you have any documentation url please share with us.

Thank You,
Nandakishore.

You can select one or more Objects in Designer, add them to a Patch, export that Patch, download that Patch (which is a Zip file). You can then introspect into that Patch and examine the XML of the Objects, where you can then find the UUID of the objects.

Here's an example from an Integration object I exported from one of my environments:

<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<contentHaul xmlns:a="http://www.appian.com/ae/types/2009">
    <versionUuid>_a-0000e684-9275-8000-9bb4-011c48011c48_650113</versionUuid>
    <outboundIntegration>
        <name>DAS_digitalPreApp</name>
        <uuid>_a-0000e684-9275-8000-9bb4-011c48011c48_616444</uuid>
        <description>Call BAP WebAPI to return some Application Details</description>
        <parentUuid>_a-0000e684-9275-8000-9bb4-011c48011c48_616438</parentUuid>
        <visibility>
            <advertise>false</advertise>
            <hierarchy>true</hierarchy>
            <indexable>true</indexable>
            <quota>false</quota>
            <searchable>true</searchable>
            <system>false</system>
            <unlogged>false</unlogged>
        </visibility>
        <definition></definition>
        <namedTypedValue>
            <name>appId</name>
            <type>
                <name>int</name>
                <namespace>http://www.w3.org/2001/XMLSchema</namespace>
            </type>
        </namedTypedValue>
        <metadataExpr></metadataExpr>
        <preferredEditor>legacy</preferredEditor>
        <offlineEnabled>false</offlineEnabled>
        <sharedConfigParameters>
            <a:Dictionary xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
                <url xsi:type="xsd:string"/>
                <isInheritedUrlOptionSelected xsi:type="xsd:boolean">true</isInheritedUrlOptionSelected>
                <relativePath xsi:type="xsd:string"/>
                <authType xsi:type="xsd:string">None</authType>
                <authDetails xsi:type="xsd:string"/>
            </a:Dictionary>
        </sharedConfigParameters>
        <configParameters>
            <a:Dictionary xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
                <contentType xsi:type="xsd:string"/>
                <automaticallyConvert xsi:type="xsd:boolean">true</automaticallyConvert>
                <shouldReceiveDocuments xsi:type="xsd:boolean">false</shouldReceiveDocuments>
                <jsonSchema xsi:nil="true" xsi:type="a:NestedChoice?list"/>
                <receiveFolderConfig xsi:type="a:Dictionary">
                    <asExpr xsi:type="xsd:boolean">false</asExpr>
                    <value xsi:type="a:Variant?list"/>
                </receiveFolderConfig>
                <bodyParseType xsi:type="xsd:string">application/json+19.3</bodyParseType>
                <parameters xsi:type="a:NameValue?list">
                    <item>
                        <a:name>appId</a:name>
                        <a:value xsi:type="a:Expression">ri!appId</a:value>
                    </item>
                </parameters>
                <method xsi:type="xsd:string">GET</method>
                <headers xsi:type="a:NameValue?list"/>
                <excludeNullHeaders xsi:type="xsd:boolean">true</excludeNullHeaders>
                <documentConfig xsi:type="xsd:string"/>
                <excludeNullParams xsi:type="xsd:boolean">true</excludeNullParams>
                <featureVersion xsi:type="xsd:int">1</featureVersion>
                <timeout xsi:type="xsd:int">10</timeout>
                <body xsi:type="xsd:string"/>
                <flattenedJsonSchema xsi:nil="true" xsi:type="a:Text?list"/>
            </a:Dictionary>
        </configParameters>
        <isWrite>false</isWrite>
        <integrationType>system.http</integrationType>
        <connectedSystemUuid>_a-0000e684-9275-8000-9bb4-011c48011c48_626887</connectedSystemUuid>
        <isConnectedSystemConnectionOptionSelected>true</isConnectedSystemConnectionOptionSelected>
        <integrationOutputs>
            <a:Dictionary xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
                <outputs xsi:type="a:IntegrationOutput?list"/>
            </a:Dictionary>
        </integrationOutputs>
    </outboundIntegration>
    <roleMap public="true">
        <role inherit="true" allowForAll="false" name="readers">
            <users/>
            <groups/>
        </role>
        <role inherit="true" allowForAll="false" name="authors">
            <users/>
            <groups/>
        </role>
        <role inherit="true" allowForAll="false" name="administrators">
            <users/>
            <groups/>
        </role>
        <role inherit="false" allowForAll="false" name="denyReaders">
            <users/>
            <groups/>
        </role>
        <role inherit="false" allowForAll="false" name="denyAuthors">
            <users/>
            <groups/>
        </role>
        <role inherit="false" allowForAll="false" name="denyAdministrators">
            <users/>
            <groups/>
        </role>
    </roleMap>
    <typedValue>
        <type>
            <name>RuleTestConfig?list</name>
            <namespace>http://www.appian.com/ae/types/2009</namespace>
        </type>
        <value>
            <el>
                <a:name/>
                <a:ruleInputTestConfigs>
                    <a:value xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:type="xsd:string"/>
                    <a:nameRef>appId</a:nameRef>
                    <a:id/>
                </a:ruleInputTestConfigs>
                <a:assertions xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:nil="true"/>
            </el>
        </value>
    </typedValue>
    <history>
        <historyInfo versionUuid="_a-0000e684-9275-8000-9bb4-011c48011c48_616519"/>
        <historyInfo versionUuid="_a-0000e684-9275-8000-9bb4-011c48011c48_620931"/>
        <historyInfo versionUuid="_a-0000e684-9275-8000-9bb4-011c48011c48_626901"/>
        <historyInfo versionUuid="_a-0000e684-9275-8000-9bb4-011c48011c48_650113"/>
    </history>
</contentHaul>

You can see the object's UUID in the element <uuid>

I have a separate question as to WHY you want this information and what you're going to use it for? The very fact that Appian isn't surfacing this to you in the native Designer suggests its not very useful information, or that Appian are not understanding the value that there might be in making the UUID visible. So what's your Use Case?