Find the area between y=sinx and y=cosx on [0, pi].?

On [0, π], the curves y = sinx and y = cosx meet at x = π/4
Then, the area between the two curves on [0, π] is the sum of the integral from 0 to π/4 of (cosx - sinx) dx and the integral from π/4 to π of (sinx - cosx) dx.

The calculation is shown below :

Yes , it's OK