you'll get cos^2thetha when you'll put 1-sin^2theta=cos^2theta. then you can expand cos^2theta as (cos2theta+1)/2...then integrate cos2theta/2 and 1/2 separately...
By plugging into , and we get:
And that's it. That's the answer. If you differentiate the new found answer with CAS(like maple) you'll get what you started with which is the given integral in the question. Hope this helps.