let $\displaystyle f$ be a Lebesgue integrable function on [0,1], and let $\displaystyle \{g_n\}$ be a sequence of bounded measurable functions on [0,1] that converges uniformly to a function $\displaystyle g$. Prove that

$\displaystyle \int_{[0,1]}g_nfdx \rightarrow \int_{[0,1]}gfdx$.

help will be appreciated so much