Well this is part of a larger problem I'm doing. The thing is that I'm checking my answer on WolframAlpha gives me a different solution. I've gone over the integral several times, but I'm unable to find my error (If there's any).

Here's the link:

integral [pi*[(2-sinx)^2 - (2-cosx)^2]] from 0 to pi/4 - Wolfram|Alpha

Thanks. (bow)