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In the y-z plane, the curve z = 1 - y² and the curve z = y² - 1 form a bounded area around y axis. It is symmetric wrt y axis. The shape of curve is parabolic.

In the y-z plane the intersection of z = 1 - y² and z = y² - 1 gives the limits of integration and define the bounded area. z = 1 - y² = y² - 1 => 2 y² = 2 => y = +1 or -1

So the cross section area is bounded between y = -1 and y = +1.

In the x-axis direction the solid has a uniform area. So the solid is a cylinder with the length in the x direction with cross section in the y-z plane.