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The region bounded by the hyperbola $x^2 - y^2=1$, the line $y=-2$ , and $y=3$ is rotated about the $y$-axis. Find the volume of the resulting solid.

Can someone point me on how to set up the equation?

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    No double integral needed for a solid rotated about a coordinate axis, see below.2012-12-23

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For a solid generated by rotating a function $x(y)$ rotated about the $y$-axis, the volume of that solid between $y=a$ and $y=b$ is given by

$\pi \int_a^b dy \: x(y)^2 $

In your case, $x(y) = \pm \sqrt{1+y^2}$, $a=-2$, and $b=3$.