Never seen THAT before :O that's so cool, I'de just do ye ol'e
\small $,Let u = sinx$\\\\ $When x = pi/4, u = 1/\sqrt{2}$\\ $When x = 0, u = 0\\\\ \therefore \frac{du}{dx} = cosx\\\\ \therefore du = dxcosx\\\\ \therefore \int_{0}^{\frac{1}{\sqrt{2}}} u^{2}du\\\\\\\\ Blah
(Don't mind me, I'm...