The graph of a continuous function $y = f ( x )$ is symmetric about the origin, and for all real numbers $x$,
$$f ( x ) = \frac { \pi } { 2 } \int _ { 1 } ^ { x + 1 } f ( t ) d t$$
When $f ( 1 ) = 1$, what is the value of
$$\pi ^ { 2 } \int _ { 0 } ^ { 1 } x f ( x + 1 ) d x$$
? [4 points]\\
(1) $2 ( \pi - 2 )$\\
(2) $2 \pi - 3$\\
(3) $2 ( \pi - 1 )$\\
(4) $2 \pi - 1$\\
(5) $2 \pi$