The integral of $\sin x$ with respect to $x$ is $-\cos x$ and the integral of $\cos y$ with respect to $x$ is $x\cos y$. So, the inner integral becomes:
$$\int_{0}^{\pi}(\sin x+\cos y) dx = -\cos x \Big|_0^\pi + x\cos y \Big|_0^\pi = -\cos \pi + \cos 0 + \pi \cos
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