Let $f ( x ) = 2 + | x | - | x - 1 | + | x + 1 | , x \in R$.\\
Consider\\
$( S 1 ) : f ^ { \prime } \left( - \frac { 3 } { 2 } \right) + f ^ { \prime } \left( - \frac { 1 } { 2 } \right) + f ^ { \prime } \left( \frac { 1 } { 2 } \right) + f ^ { \prime } \left( \frac { 3 } { 2 } \right) = 2$\\
$( S 2 ) : \int _ { - 2 } ^ { 2 } f ( x ) d x = 12$\\
Then,\\
(1) both ( $S 1$ ) and ( $S 2$ ) are correct\\
(2) both $( S 1 )$ and $( S 2 )$ are wrong\\
(3) only ( $S 1$ ) is correct\\
(4) only ( $S 2$ ) is correct