Answer
$$\frac{46}{3}$$
Work Step by Step
\begin{align*}
\int_{-3}^{3} | x^2-4|dx& = \int_{-3}^{2}( x^2-4)dx-\int_{2}^{3}( x^2-4)dx\\
&= \frac{x^{3}}{3}-\left.4 x\right|_{-3} ^{2}+4 x-\left.\frac{x^{3}}{3}\right|_{2} ^{3} \\
&= \frac{46}{3}
\end{align*}