Answer
$\dfrac{9}{2}$
Work Step by Step
Our aim is to integrate the integral as follows:
$ Area =\iint_D dA $
$\int^{2}_{-1} \int^{y+2}_{y^2} \space dx \space dy = \int^{2}_{-1} [x]_{y^2}^{y+2} \space dy $
or, $=\int_{-1}^2 y+2 -y^2 \space dy $
or, $=[\dfrac{1}{2}y^2+2y -\dfrac{1}{3}y^3]_{-1}^2$
or, $=\dfrac{10}{3}-(\dfrac{-7}{6})$
or, $ Area=\dfrac{9}{2}$
