Volume of the solid whose base is the region enclosed by y=x^2 and y=1 with square cross sections

Question

I am trying to calculate the volume between $y=x^2$ and $y=1$ that has square cross-sections. It would look like a hump with curved sides and square edges.

This is the integral I thought would calculate the volume:

$$\int_{-1}^1(1-x^2)^2dx = \frac{16}{15} \approx 1.066667$$

But I think that it is wrong. Is that answer correct?