How to find out the riemann integral of following function?

Question

Let $\chi_A(x)$ denote characteristics function of $A$. Consider $$f(x) = \sum_{n=1}^{\infty} \frac{1}{n^6} \chi_{[0, n/200]} (x), \quad x \in [0,1]$$Then how to prove $f(x)$ is Riemann integrable on $[0,1]$.

I am able to prove that $f$ is not continuous on $[0,1]$.

Answer 1

It's Riemann integrable because it's bounded, $\le\zeta(6)=\pi^6/945,$ and continuous a.e. (in fact everywhere except $x=n/200$).