Volume of the region between two parabolas?

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Homework Statement

Find the volume of the region enclosed by z = 1 - y^2 and z = y^2 - 1 for x lying between 0 and 2 inclusive.

Homework Equations

The Attempt at a Solution

I know that the y bounds are from -1 to 1, where the parabolas meet. x bounds are from 0 to 2. So would the integral simply by the double integral , x from 0 to 2, y from -1 to 1 of the (y^2 -1) - (1 - y^2)? I'm confused at this point. All the limits of integration are constant..

 

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Ah no worries, found out how to solve it! I expressed the x coordinate as f(y,z)=2. Then integrated this function with respect to y and z, with the bounds I specified. Thanks!