Answer
$A$ = $\frac{9}{4}$
Work Step by Step
$A$ = $\int_{-2}^{-\frac{1}{2}}[(x^{2}+2x)-(x^{2}+x-2)]dx$ + $\int_{-\frac{1}{2}}^{1}[(x^{2}-1)-(x^{2}+x-2)]dx$
$A$ = $\int_{-2}^{-\frac{1}{2}}[x+2]dx$ + $\int_{-\frac{1}{2}}^{1}(-x+1)dx$
$A$ = $(\frac{1}{2}x^{2}+2x)|_{-2}^{-\frac{1}{2}}$ + $(-\frac{1}{2}x^{2}+x)|_{-\frac{1}{2}}^{1}$
$A$ = $\frac{9}{4}$
