Question about a double integral.

[DavidAp]

The double integral xcosy is bounded by y=0, y=x^2, and x=1. I was able to integrate almost wholly through; however, toward the end I was unsure what to do when i was asked to plug in x^2 into x^2. What do I do?!

Here is an image of my work on the white board. Please, if my hand writing is illegible tell me and I would be more than happy to type it all out for you.
Thank you for taking the time to review my question.

 

[QuarkCharmer]

Here you go, you can remove that giant image via edit.

 

[DavidAp]

Thank You!

I solved it after a triple glance at the board! I knew something had to be wrong so I change my first integral to be 0 -> 1 and it worked! I'm just putting this out there because I don't know how to delete a thread, but thank you anyways forum!