Finding the volume of a region using spherical coordinates

I am trying to find the volume of the region bounded by $z=0, z=y^2, x=-1, x=1, y=-1, y=1$ using spherical coordinates.

I realize that I don’t need spherical coordinates to compute the volume since I can find it by evaluating $$int_{x=-1}^{1}int_{y=-1}^{1}int_{z=0}^{y^2} mathrm{dz}, mathrm{dy} , mathrm{dx}$$ I am just curious about how it can be computed using spherical coordinates. However, I can’t really find the integration bounds. I don’t think it can be computed in a single integral (not sure), so I tried to split the volume into pieces. I didn’t get anywhere.