Answer
$U = 19.3~J$
Work Step by Step
We can find the potential energy at $~~x = 2.0~m$:
$\Delta U = -\int_{0}^{2.0}~F(x)~dx$
$\Delta U = -\int_{0}^{2.0}~(-3.0~x-5.0~x^2)~dx$
$\Delta U = \int_{0}^{2.0}~(3.0~x+5.0~x^2)~dx$
$\Delta U = (1.5~x^2+\frac{5.0~x^3}{3})\Big \vert_{0}^{2.0}$
$\Delta U = [1.5~(2.0)^2+\frac{(5.0)~(2.0)^3}{3}]-0$
$\Delta U = 19.3~J$
Since $~~U=0~~$ at $~~x = 0,~~$ then $~~U = 19.3~J~~$ at $~~x = 2.0~m$
