Answer
$$\dfrac{40 \pi}{3}$$
Work Step by Step
Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_{0}^{2} (2 \pi) \cdot y (y^2-(-y)) dy \\=2 \pi \times (\dfrac{y^4}{4}+\dfrac{y^3}{3})_{0}^{2} \\=\dfrac{40 \pi}{3}$$
