I am trying to find the volume generated by rotating the region bounded by $\displaystyle y=4+x-x^2$ and $\displaystyle y=4-x$ about the y-axis

I got an answer of $\displaystyle 4\pi/3$

using this: $\displaystyle \pi \int_0^2 (4+x-x^2)-(4-x)$

I feel as if this volume is to small but since is rotated about the y-axis I dont have any other values to add that I can think of to account for the area rotated not touching the y-axis.