How do I prove that the SBAF activation function is not a probability density function?

Question

The SBAF activation function is as follows - Note : 0<=x<=1 $$ f(x) = \frac{1}{1+ kx^a(1-x)^{1-a}} $$ Where k and a are constants. I know we have to show that integral $\int_{-\infty}^{\infty} f(x)\, dx$ is not equal to 1. But I'm not able to integrate this. Can someone help me out ?

Answer 1

$0\leq f(x) \leq 1$ for all $x \in (0,1)$. So $\int_0^{1}f(x)dx \leq 1$ and equality can hold only of $f(x)=1$ for all $x$. But $f(x) \neq 1$ for any $x \in (0,1)$!.