Answer
$$\dfrac{108 \pi}{5}$$
Work Step by Step
We need to integrate the integral to compute the volume.
We have:
Area $=(R^2- r^2) \pi=\pi (12+4x-9x^2+x^4)$
Now,
$$Volume= \pi \times \int_{-1}^{2} (12+4x-9x^2+x^4) \space dx \\= (24+8-24+(32/5)+12-2-3+\dfrac{1}{5}) \times \pi \\= \pi (15+\dfrac{33}{5} ) \\=\dfrac{108 \pi}{5}$$
