I integrated my JIRA project with TestLink using http://blogs.quovantis.com/step-by-step-integration-of-jira-with-testlink/.
However, there is no way on JIRA to understand that TestLink is integrated successfully and vice-versa.
As with TestRail, when integrated with JIRA, I could see the "TestRail" tab on JIRA dashboard. Also, in TestRail while creating Test cases I could see separate field "References" to add JIRA ID reference. Upon adding reference, test case ID gets reflected in same JIRA ID as well.
Check the image for reference.
How to check whether TestLink is integrated with JIRA?
