Thanks a for the help everyone!
I came across another one that has stumped me:
The integral from -1 to 1: sinx / 1 + x^2 dx
I see 1 / 1+x^2 as the derivative of arctan, but I'm not sure if that is relevant. The only this I could think of was to integrate by parts, but after attempting that, I seem to just be going in circles.