Let $f ( x ) = | x - 4 |$

Multiple Choice

Let $f ( x ) = | x - 4 |$ If $c \in ( 0,2 )$ such that $\frac { \int _ { 0 } ^ { 2 } | x - 4 | d x } { 2 } = f ( c ) ,$ then c is

A) $\frac { 1 } { 2 }$
B) $\frac { 2 } { 3 }$
C) 1
D) $\frac { 4 } { 3 }$
E) $\frac { 5 } { 4 }$