Need help with the limits of $y$ in a double integral.

Question

I am asked to calculate the volume of the region bounded by the surface $z=x^2-y^2$, the $xy$-plane and the planes $x=1$ and $x=3$. I want to set up the integral as follows: $$\mathrm{Vol} = \int_1^3\left(\int_{y=y_1}^{y=y_2}x^2-y^2dy\right)dx$$but I'm having trouble determining $y_1$ and $y_2$. I've plotted the function but it wasn't of much help. Any insight will be appreciated.

Answer 1

$$\mathrm{Vol} = \int_1^3\left(\int_{-x}^{x}x^2-y^2dy\right)dx$$

Consider at a fixed $x$, $z=x^2-y^2$; this is a parabola in the $yz$ plane. $z:0\to x^2-y^2$ and $y:-x \to x$