$\displaystyle x+y=1$

$\displaystyle x=5-(y-2)^2$

Rotate around the x-axis, using the cylindrical shell method

This is what ive came up with but its wrong

$\displaystyle 2\pi\int_0^5 ((5-(y-2)^2+(1-y))(1-y) = \frac{145\pi}{6}$

Any help appreciated, thanks