Let $f(x)= \begin{cases} \sin \left(\frac{\pi}{x} \right) &\text{ if } 0 < x < 1\\ 0 &\text{ if } x=0 \end{cases}$
Prove that $f$ is Riemann integrable on $[0, 1]$.
I know a function is considered Riemann integrable if it is continuous and bounded. In this case, f is continuous on the interval $[-1, 1]$ and is also bounded. I'm inclined to believe this answer would satisfy the question. Is this enough or is there more I could prove?
This is page $82$ question $3.27$ of Advanced Calculus: An Introduction to Linear Analysis by Leonard Richardson.