# Convergent series in 0 1/Riemann-integrable function/Series of integrals to a n/Exercise

Let ${\displaystyle {}\sum _{n=1}^{\infty }a_{n}}$ be a convergent series with ${\displaystyle {}a_{n}\in [0,1]}$ for all ${\displaystyle {}n\in \mathbb {N} }$ and let ${\displaystyle {}f\colon [0,1]\rightarrow \mathbb {R} }$
${\displaystyle \sum _{n=1}^{\infty }\int _{0}^{a_{n}}f(x)dx}$