Problem on using the definition of Riemann Integral

Problem on using the definition of Riemann Integral

Consider the function: $f:[a,b]\rightarrow \mathbb{R}$ be a bounded
function on $[a,b]$. Suppose that $f$ is Riemann integrable on $[a,c]$ for
any $c\in (a,b)$. The question is to prove that $f$ is Riemann integrable
on the interval $[a,b]$.
I am completely stuck on this question. I tried to use the tagged
partition notion for Riemann integrals, but I couldn't figure out a way to
start solving it. I appreciate any help!