Consider this statement about a function $f ( x )$ :
$\left( ^ { * } \right)$ If $( f ( x ) ) ^ { 2 } \leq 1$ for all $- 1 \leq x \leq 1$ then $\int _ { - 1 } ^ { 1 } ( f ( x ) ) ^ { 2 } \mathrm {~d} x \leq \int _ { - 1 } ^ { 1 } f ( x ) \mathrm { d } x$
Which one of the following functions provides a counterexample to (*)?