Find the Coefficient Of $x ^ { 5 }$ In the Maclaurin Series For

Multiple Choice

Find the coefficient of $x ^ { 5 }$ in the Maclaurin series for $f ( x ) = \int \cos \left( x ^ { 2 } \right) d x$ .Note: The series is unique except for the constant of integration.

A) $- \frac { 1 } { 10 }$
B) $\frac { 1 } { 15 }$
C) $- \frac { 1 } { 5 }$
D) $\frac { 2 } { 5 }$
E) $- \frac { 2 } { 5 }$
F) $- \frac { 1 } { 15 }$
G) $\frac { 1 } { 5 }$
H) $\frac { 1 } { 10 }$