$\lim_{n \rightarrow \infty} \prod_{k=1} ^ n \left( 1+ \frac{1}{n}f\left(\frac{k}{n}\right) \right)= e^{\int_0 ^1 f(x)dx} $

Question

I have been trying to show that if $f:[a,b]\rightarrow \mathbb{R}$ is a continuous function then $$\lim_{n \rightarrow \infty} \prod_{k=1} ^ n \left( 1+ \frac{1}{n}f\left(\frac{k}{n}\right) \right)= e^{\int_0 ^1 f(x)dx} $$

I have tried some approaches to prove this but couldn't find a way. Can someone kindly help me out. Thank you.