Let the function
$$f ( x ) = x ^ { 3 } - | x | + 2$$
a) ( 0.75 points) Study the continuity and differentiability of $f$ at $x = 0$.
b) (1 point) Determine the relative extrema of $f ( x )$ on the real line.
c) ( 0.75 points) Calculate the area of the region bounded by the graph of $f$, the x-axis $y = 0$, and the lines $x = - 1$ and $x = 1$.