Answer
$$\dfrac{117 \pi}{5}$$
Work Step by Step
We need to integrate the integral to compute the volume.
We have:
$$Area =(R^2- r^2) \pi=\pi (8+6x-x62-x^4)$$
Now, $$Volume = \int_{-1}^{2} (8+6x-x^2-x^4) \space dx \times \pi\\= \pi \space [8+3x^2-\dfrac{x^3}{3}-\dfrac{x^5}{5}]_{-1}^{2} \\= \pi (30-\dfrac{33}{5}) \\=\dfrac{117 \pi}{5}$$
