Hello. I need help in finding of the indefinite integral of

$\displaystyle \int{Sin^2(sinx)+Cos^2(cosx)} dx$ from 0 to p/2.

I've started from reducing squares by $\displaystyle sin(cosx)=(1-Cos(2cosx))/2$. the same with cos

And then I used universal trigonometric substituon. And I got 3 integrals, two of those are really difficult to solve.

Am I on a right way? Is there any easier way? Because I don't know how to find 1 integral I've got.