Let $f ( x ) = x ^ { 3 }$

Multiple Choice

Let $f ( x ) = x ^ { 3 }$ If $c \in ( - 1,1 )$ such that $\frac { \int _ { - 1 } ^ { 1 } x ^ { 3 } d x } { 2 } = f ( c ) ,$ then c is

A) $- \frac { 1 } { 4 }$
B) $- \frac { 1 } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 2 }$
E) 0