Answer
FALSE
Work Step by Step
Given:$\int_{a}^{b}\sqrt {f(x)}dx=\sqrt {\int_{a}^{b}f(x)dx}$
Consider $f(x)=1,, a=0, b=4$
Therefore,
$\int_{0}^{4}\sqrt {1}dx=\sqrt {\int_{0}^{4}(1)dx}$
Thus, $4\ne\sqrt4 $
Hence, $\int_{a}^{b}\sqrt {f(x)}dx\ne\sqrt {\int_{a}^{b}f(x)dx}$
The given statement is false.