Volume of Solid Bounded by the cylinders $y=x^2$ and $y=z^2$ and the plane $y=1$ Find the volume of the solid bounded by the cylinders $y=x^2, y=z^2$ and the plane $y=1$
I think the integral should be: $$\int_0^1\int_{-\sqrt y}^\sqrt y\int_{-\sqrt y}^\sqrt y\ dx\,dz\,dy$$
Could someone tell me if this is correct?

This is not quite right. The region of integration there is not curved but straight like this:

Instead, maybe to

 use cylindrical coordinates.

Also please look at this question here: Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. (using disk/washer).
