Answer
$-72$
Work Step by Step
Since $x$ is odd and $x^2 $ is an even function, then
\begin{align*}
\int_{-3}^{3}\left(9 x-4 x^{2}\right) d x&=9\int_{-3}^{3} x-4 \int_{-3}^{3}x^{2} d x\\
&=9(0)-8\int_{0}^{3}x^2dx\\
&= -8\frac{x^3}{3}\bigg|_{0}^{3}\\
&=-72
\end{align*}
