Answer
-3
Work Step by Step
Take the antiderivative of $x^{2}$-4x+2 to get $\frac{1}{3}$$x^{3}$-$\frac{4}{2}$$x^{2}$+2x. This simplifies to $\frac{1}{3}$$x^{3}$-2$x^{2}$+2x. Plug in the upper and lower bounds to get [$\frac{1}{3}$$4^3$-2($4^2$)+2(4)] - [$\frac{1}{3}$$1^3$-2($1^2$)+2(1)]. This simplifies to [$\frac{64}{3}$-32+8] - [$\frac{1}{3}$-2+2]. Finally, we simplify to [$\frac{64}{3}$-$\frac{72}{3}$] - [$\frac{1}{3}$], which equals $\frac{-9}{3}$ or -3.
