Answer
Area= $\frac{32}{3} $
Work Step by Step
Find the points of intersection
$-x+1= -x^2 + 3x+1$
$x=0,4$
Setup the integration using 0 and 4 as the limits of integration
$\int^4_0 [(-x^2 + 3x+1)- (-x+1)]dx$
$\int^4_0 (-x^2 + 4x)dx$
$ [-\frac{1}{3}x^3 + 2x^2]^4_0$
$\frac{32}{3} - 0$
$\frac{32}{3} $
