Given the function $f ( x ) = \sin \left( \frac { \pi } { 2 } x \right)$, it is requested:
a) ( 0.5 points) Study the parity of the function $g ( x ) = f ( x f ( x ) )$.
b) (1 point) Calculate $\lim _ { x \rightarrow 0 } \frac { \sqrt { 4 + 3 f ( x ) } - 2 } { x }$.
c) (1 point) Calculate $\int _ { 0 } ^ { 1 } x f ( x ) d x$.