Consider the function $h : ]0,1[ \longrightarrow \mathbf{R},\; t \longmapsto \frac{1}{\sqrt{t(1-t)}}$. Prove that: $$\lim_{n \longrightarrow +\infty} \sum_{k=1}^{2n-1} \frac{1}{2n} h\!\left(\frac{k}{2n}\right) = \int_0^1 h(t)\, dt.$$