Answer
$$\dfrac{ 4\pi}{3}$$
Work Step by Step
Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\ = \int_{0}^{1} (2 \pi) \times y \times (y+y) \space dy \\=(4 \pi) \times [\dfrac{y ^3}{3}]_{0}^{1} \\ =\dfrac{ 4\pi}{3}$$
