Okay so the question goes

For x in [-pi/2,pi/2], define $\displaystyle I(x)=\int_{sin(x)}^{cos(x)}\frac {1} {t+(\sqrt(1-t^2))} dt $

Find I(x) by showing that dI/dx = -1 and that I(pi/4)=0.

I have the done the first part, ie showing that dI/dx= -1 and that I(pi/4)=0. However, I can't figure out how to use my answer to that part to find I(x). Can anyone help?