The area of the region (x, y): x^2 +y^2≤1≤x+y is :

$\left(\frac{\pi}{4}-\frac{1}{2}\right)$

$\left(\frac{\pi}{4}+\frac{1}{2}\right)$

$\left(\frac{\pi}{2}-\frac{1}{2}\right)$

$\left(\frac{\pi}{2}+\frac{1}{2}\right)$