Answer
$\frac{9}{2}$
Work Step by Step
Setup the integration to find the area between f(x) and g(x)
f(x) and g(x) intersect at x=-2, 1
$\int_{-2}^1 [(x+2)-(x^2+2x)]dx$
$\int_{-2}^1 (-x^2 -x+2)dx$, Integrate
$[-\frac{1}{3}x^3 - \frac{1}{2}x^2 +2x]_{-2}^1$, Evaluate the definite integral
$ (-\frac{1}{3} -\frac{1}{2} +2)-(\frac{8}{3}-2-4)$
$\frac{9}{2}$
