Choose the integral which represents the volume of the solid generated by rotating the region $x^2+(y-1{)}^2=1,$ given on the picture, about the $y-$axis.

$\backslash$table$[[$A: ${\displaystyle \underset{0}{\overset{2}{}}}(2y-y^2)dy,$B: ${\displaystyle \underset{0}{\overset{2}{}}}(x^2-2x)dx,$C: ${\displaystyle \underset{0}{\overset{2}{}}}(y-1{)}^{2}dy$