Answer
$\dfrac{9}{2}$
Work Step by Step
Our aim is to integrate the integral as follows:
$ Area =\iint_D dA $
$\int^{1}_{-2} \int^{-y^2}_{y-2} \space dx \space dy= \int^{1}_{-2} (-y^2-(y-2) \space dy $
or, $=[\dfrac{-y^3}{3}-\dfrac{y^2}{2}+2y]^1_{-2}$
or, $=(\dfrac{-1}{3}-\dfrac{1}{2}+2)-(\dfrac{8}{3}-\dfrac{4}{2}-4)$
or, $=\dfrac{9}{2}$