In the rectangular coordinate plane, the region between the parabola $y = x ^ { 2 }$, the line $x = 1$, and the line $y = 0$ is shown.
What is the volume in cubic units of the solid of revolution obtained by rotating this region $360 ^ { \circ }$ about the line $\mathbf { y = - 1 }$?\\
A) $\frac { 3 \pi } { 4 }$\\
B) $\frac { 5 \pi } { 8 }$\\
C) $\frac { 7 \pi } { 10 }$\\
D) $\frac { 11 \pi } { 12 }$\\
E) $\frac { 13 \pi } { 15 }$