Double Integrating an Absolute Function

Having difficulty solving this one:

$\displaystyle \int\int_D|cos(x+y)|dA$ for $\displaystyle 0 \leq x \leq \pi$ and $\displaystyle 0 \leq y \leq \pi$.

For the first partition, I integrated

$\displaystyle \int_{0}^{\frac{\pi}{2}}\int_{0}^{\frac{\pi}{2}-x}}cos(x+y)dydx $ and got $\displaystyle \frac{\pi}{2}-1. $

For the next integral I obtained $\displaystyle \frac{\pi}{2} \leq x \leq \pi$ and $\displaystyle \frac{\pi}{2}-x \leq y \leq \pi - x$ as my bounds which is incorrect according to the solution I was given, can someone lead me from here?