The area of the region $\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

Question

The area of the region

$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

$\frac{5}{2} \sin ^{-1}\left(\frac{3}{5}\right)-\frac{1}{2}$

$\frac{5 \pi}{4}-\frac{3}{2}$

$\frac{3 \pi}{4}+\frac{3}{2}$

$\frac{5 \pi}{4}-\frac{1}{2}$

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