Let $f(x)=c$ for all $x$ in $[a,b]$ and some real number $c$. Show by definition below that $f$ is Riemann integrable on $[a,b]$, and $\int f(x) dx = c(b-a)$.
Definition: A function $f$ is Riemann integrable on $[a,b]$ if there is a real number $R$ such that for any $\varepsilon > 0$, there exists $\delta > 0$ such that for any a partition $P$ of $[a,b]$ satisfying $\|P\|< \delta$, and for any Riemann sum $R(f,P)$ of relative to $P$, we have $|R(f,P)-R|< \varepsilon$