If $f(x)=\large\frac{A}{\pi}\frac{1}{16+x^{2'}}$$-\infty<x<\infty$\[\]is a p.d.f of a continuous random variable $X,$ then the value of $A$ is

Question

\[\begin{array}{1 1}(1)16&(2)8\\(3)4&(4)1\end {array}\]