Is it only GUI testing?
No, it's up to you. Personally, I create automation tests for the test cases that are often executed, and the test that is simple (not complex).
Do we also have to create Integration automation scripts?
Yes, we do. It is part of testing and hence the testers' job.
What would be our boundaries when a developer also does their own testing(unit, component/integration)?
From my experience, there are no boundaries. Developers and Testers have to work together to maintain test scripts because it is the most time-consuming tasks. By the way, I usually ask developers to do unit testing, and I will create GUI tests for them, then we help each other to maintain test scripts.