Answer
$2 \pi^2$
Work Step by Step
Our aim is to find the area between the two given functions $y_1=\sin x$ and $y_2=x$.
This can be computed as;
$Area=|\int_a^b (y_2-y_1)\ dx|\\=|\int_0^{2\pi} (\sin x-x)\ dx|\\=[\cos x-\dfrac{1}{2} x^2]_0^{2 \pi}\\=[\cos 2\pi-\cos (0)]-\dfrac{4 \pi^2}{2}\\=2 \pi^2$
