Expressing Limit as Riemann Integral

Question

Ive got another question:

Express the limit $lim_{n\to\infty}\sum_{k=1}^n\frac{\pi}{n}sin(\frac{\pi k}{n})$ as a Riemann Integral

I have the knowledge of Riemann Integrals but cant apply it to this question. Any help will be appreciated.

Answer 1

Observe \begin{align} \sum^n_{k=1} \frac{\pi}{n} \sin\left(\frac{\pi k}{n} \right) \approx \int^1_0 \pi \sin \pi x\ dx. \end{align}