Answer
$$\dfrac{\pi}{30}$$
Work Step by Step
We need to integrate the integral to compute the volume.
$$Volume= \int_{0}^{1} \pi (x^2-2x^3+x^4) \space dx \\ =[\dfrac{x^3}{3}-\dfrac{2x^4}{4}+\dfrac{x^5}{5}]_0^1 \\=\dfrac{(\pi)}{3}-\dfrac{(\pi)}{2}+\dfrac{(\pi)}{5} \\=\dfrac{\pi}{30}$$
