Step 1: define "integrate"
Step 2: Using that definition, work out what you want ServiceNow to do in terms of read/write with JIRA data. This should lead you to understand where you need to code in ServiceNow, then you can look at JIRA's REST API to work out how to do it.
Step 3: Using that definition, work out what you want JIRA to do in terms of read/write with ServiceNow data. This should lead you to understand where you need to code in JIRA, then you can look at stuff ServiceNow exposes to work out how to do it
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