Consider the functions defined implicitly by the equation $y ^ { 3 } - 3 y + x = 0$ on various intervals in the real line. If $x \in ( - \infty , - 2 ) \cup ( 2 , \infty )$, the equation implicitly defines a unique real valued differentiable function $y = f ( x )$. If $x \in ( - 2,2 )$, the equation implicitly defines a unique real valued differentiable function $y = g ( x )$ satisfying $g ( 0 ) = 0$. $\int _ { - 1 } ^ { 1 } g ^ { \prime } ( x ) d x =$ (A) $2 g ( - 1 )$ (B) 0 (C) $- 2 g ( 1 )$ (D) $2 g ( 1 )$
Consider the functions defined implicitly by the equation $y ^ { 3 } - 3 y + x = 0$ on various intervals in the real line.\\
If $x \in ( - \infty , - 2 ) \cup ( 2 , \infty )$, the equation implicitly defines a unique real valued differentiable function $y = f ( x )$.\\
If $x \in ( - 2,2 )$, the equation implicitly defines a unique real valued differentiable function $y = g ( x )$ satisfying $g ( 0 ) = 0$.
$\int _ { - 1 } ^ { 1 } g ^ { \prime } ( x ) d x =$\\
(A) $2 g ( - 1 )$\\
(B) 0\\
(C) $- 2 g ( 1 )$\\
(D) $2 g ( 1 )$