The Particular Solution of the Differential Equation $\frac { d y } { d x } = x ^ { 2 } + 2 x + 1$

Multiple Choice

The particular solution of the differential equation $\frac { d y } { d x } = x ^ { 2 } + 2 x + 1$ satisfying the boundary condition when x = 3, y = -1 is

A) $y = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } + x - 3$
B) $y = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } + x + 1$
C) $y = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } + x - 22$
D) $y = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } + x - 21$
E) $y = \frac { 1 } { 3 } x ^ { 3 } + x ^ { 2 } + x - 23$