I need to setup and evaluate the integral that gives volume of the solid formed by revolving around the region about the y-axis.

$\displaystyle x=-y^2+4y$

Volume =Pi r^2 So the Intergral evaluated from 4 to 1(guessing)V=Pi $\displaystyle (-y^2+4y)^2dy$ after the algebra I get $\displaystyle y^4-8y^3+16y^2$ My question is do I use $\displaystyle y^5/5-8y^4/4+16y^3/3$ to evaluate from 1 to 4?