Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 321: 61

$\pi$

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$