$\lim_{r\to 0}\int_{-K}^K f(rx)dx=\int_{-K}^K \lim_{r\to 0} f(rx)dx$.

$\lim_{r\to 0}\int_{-K}^K f(rx)dx=\int_{-K}^K \lim_{r\to 0} f(rx)dx$.

When is this true? $\lim_{r\to 0}\int_{-K}^K f(rx)dx=\int_{-K}^K
\lim_{r\to 0} f(rx)dx$. Is it true without the hypothesis of continuity of
f? Thank you.