Determine Whether the Function Is a Probability Density Function Over $$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { \pi \left( x ^ { 2 } + 1 \right) } & x \geq 0 \\0 & x < 0\end{array} \right.$$

True/False

Determine whether the function is a probability density function over the given interval.
- $$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { \pi \left( x ^ { 2 } + 1 \right) } & x \geq 0 \\0 & x < 0\end{array} \right.$$