# Is there any bound for $\int_{\mathbb{R}}\sqrt{f_0[x]f_1[x]}\mbox{d}x$

I wonder if there is an upperbound for following the expression:

$$\int_{\mathbb{R}}\sqrt{f_0[x]f_1[x]}\mbox{d}x$$

where $f_i$, $i=0,1$ are some density functions.

1. Use Cauchy Schwarz.$\mbox{ }$