The function $h$ is differentiable, and for all values of $x$, $h ( x ) = h ( 2 - x )$. Which of the following statements must be true?
I. $\int _ { 0 } ^ { 2 } h ( x ) d x > 0$
II. $h ^ { \prime } ( 1 ) = 0$
III. $h ^ { \prime } ( 0 ) = h ^ { \prime } ( 2 ) = 1$
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III