$\begin{aligned} & \int_{-2}^2 3\left|x^2-x-2\right| d x \\ & =3 \int_{-2}^2\left|x^2-x-2\right| d x \\ & =3\left[\int_{-2}^{-1}\left(x^2-x-2\right) d x+\int_{-1}^2-\left(x^2-x-2\right) d x\right] \\ & =3\left[\left.\left(\frac{x^3}{3}-\frac{x^2}{2}-2 x\right)\right|_{-2} ^1-\left(\frac{x^3}{3}-\frac{x^2}{2}-2 x\right)_{-1}^2\right] \\ & =3\left[7-\frac{2}{3}\right] \\ & =19\end{aligned}$