solved. not sure how to delete a thread. thanks!
$\displaystyle \int f(x) \ dx = \frac{x^4}{4} + \frac{10}{3}x^{\frac{3}{2}} + C $
$\displaystyle F(1) = -6 \implies -6 = \frac{1}{4} + \frac{10}{3} + C $, $\displaystyle C = \frac{43}{12} + 6 $
$\displaystyle \int f(x) \ dx = \frac{x^4}{4} + \frac{10}{3}x^{\frac{3}{2}} + \boxed{\frac{115}{6}} $