The Area of the Region That Lies to the Right $x=6 y-y^{2}$

Multiple Choice

The area of the region that lies to the right of the y-axis and to the left of the parabola $x=6 y-y^{2}$ (the shaded region in the figure) is given by the integral $\int_{0}^{5}\left(6 y-y^{2}\right) d y$ . Find the area..

A) $17.5$
B) $12.5$
C) $10.25$
D) $\frac{275}{6}$
E) $\frac{25}{6}$