A polynomial function $f ( x )$ satisfies the following conditions.\\
(가) For all real numbers $x$,
$$\int _ { 1 } ^ { x } f ( t ) d t = \frac { x - 1 } { 2 } \{ f ( x ) + f ( 1 ) \}$$
(나) $\int _ { 0 } ^ { 2 } f ( x ) d x = 5 \int _ { - 1 } ^ { 1 } x f ( x ) d x$\\
When $f ( 0 ) = 1$, find the value of $f ( 4 )$. [4 points]