Answer
$$\dfrac{2}{3}$$
Work Step by Step
Our aim is to integrate the triple integral as follows:
$$ V=\int^1_0 \int^1_{-1} \int^{y^2}_0 \space dz \space dy \space
dx \\= \int^1_0 \int^1_{-1}y^2 dy \space dx \\=\dfrac{2}{3} \times \int^1_0 dx \\=\dfrac{2}{3}$$
