Answer
$\int_{-4}^{2}[f(x)+2x+5]~dx = 15$
Work Step by Step
We can evaluate the integral:
$\int_{-4}^{2}[f(x)+2x+5]~dx$
$= \int_{-4}^{2}f(x)~dx+\int_{-4}^{2}2x~dx+\int_{-4}^{2}5~dx$
$= \int_{-4}^{2}f(x)~dx+2\int_{-4}^{2}x~dx+\int_{-4}^{2}5~dx$
$= (-3+3-3)+2[\frac{(2)^2-(-4)^2}{2}]+5[2-(-4)]$
$= (-3)+(-12)+(30)$
$= 15$
