$f ( x )$ is a function defined for all real values of $x$.
Which one of the following is a sufficient condition for $\int _ { 1 } ^ { 3 } f ( x ) d x = 0$ ?
A $f ( 2 ) = 0$
B $f ( 1 ) = f ( 3 ) = 0$
C $f ( - x ) = - f ( x )$ for all $x$
D $f ( x + 2 ) = - f ( 2 - x )$ for all $x$
E $\quad f ( x - 2 ) = - f ( 2 - x )$ for all $x$