r=cos(t) r=sin(t)

find the area of intersection.

I come up with integrals of cos^2 t - sin^2 t from 0 to pi/4, and from 5pi/4 to 2pi, sin^2 t - cos^2 t from pi/4 to 5pi/4.

is that correct and, is there a simpler way to tackle the problem?

Thank you very much!