The Area of the Region That Lies to the Right $y$

Multiple Choice

The area of the region that lies to the right of the $y$ -axis and to the left of the parabola $x = 2 y - y ^ { 2 }$ (the shaded region in the figure) is given by the integral $\int _ { 0 } ^ { 2 } \left( 2 y - y ^ { 2 } \right) d y$ .
Find the area..

Select the correct answer.

A) $\frac { 175 } { 6 }$
B) 4
C) 9
D) $\frac { 4 } { 3 }$
E) 6