Let $f ( u ) = \tan ^ { - 1 } ( u )$, a function whose domain is the set of all real numbers and whose range is $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$. Let $g ( v ) = \int _ { 0 } ^ { v } f ( t ) \, d t$.
(a) $f ( 1 ) = \frac { \pi } { 4 }$.\\
(b) $f ( 1 ) + f ( 2 ) + f ( 3 ) = \pi$.\\
(c) $g$ is an increasing function on the entire real line.\\
(d) $g$ is an odd function, i.e., $g ( - x ) = - g ( x )$ for all real $x$.