Answer
$\pi$
Work Step by Step
We need to find the area of the rectangle with limits $0$ to $\pi$.
$A=\int_0^{\pi} (1+\cos x ) dx$
This implies that
$[x+\sin x]_0^{\pi}=(\pi+\sin \pi)-(0+\sin 0)$
or, $(\pi+\sin \pi)-(0+\sin 0)=\pi$
Thus, the area of the shaded region is: $ 2 \pi-\pi =\pi$