Answer
A=$10$
Work Step by Step
Setup the integration to find area between the two functions
$\int_{-1}^1 [(-x^3 +2)-(x-3)]dx$
$\int_{-1}^1 (-x^3 -x+5)dx$, Integrate
$[-\frac{1}{4}x^4 - \frac{1}{2}x^2 +5x]_{-1}^1$, Evaluate the definite integral
$(-\frac{1}{4} -\frac{1}{2} +5) - ( -\frac{1}{4} - \frac{1}{2} - 5)$
$A=10$
