Answer
$$F(x)=x^6-\frac{8}{5}x^5-3x^3+C$$
Work Step by Step
Given $$f(x) =6x^5-8x^4-9x^2$$
Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$
\begin{align*}
F(x) &=\frac{6x^6}{6}-\frac{8x^5}{5}-\frac{9x^3}{3}+C\\
&= x^6-\frac{8}{5}x^5-3x^3+C
\end{align*}
To check
\begin{align*}
F'(x) &=6x^5-8x^4-9x^2\\
&=f(x)
\end{align*}
