Volume of revolution setup I've been given a question as so

Consider the region $R = \{(x,y)\; |\; 0 ≤ y \;and \;y^2≤ x ≤ y+2\}$
Draw R and calculate the exact volume by rotating the region R about the line x=0

So this is what $R$ looks like (shaded in black).. I think.
And the equation I came up with was to integrate from 0 to 2, of the equation $π((y+2)-y^2)^2 \;dy$
Is this correct? I've never attempted a question setup like this before.
Thank you so much!

Close. Just remember that:
$$
\pi(R - r)^2 \neq \pi(R^2 - r^2)
$$
So the correct setup is:
$$
V = \pi\int_0^2 \left[(y + 2)^2 - (y^2)^2 \right] \, dy
$$
