Can we interchange Trace and Integral because both are linear operator?

Question

Is it true if we write the following and interchange Trace and Integral operators

$$ \int_a^b Tr(r(x)r(x)^T)dx = Tr(\int_a^br(x)r(x)^Tdx) $$

where $r(x) \in \mathbb{R}^n$ and $a,b \in \mathbb{R}$.