Consider the function $h : ]0,1[ \longrightarrow \mathbf{R},\; t \longmapsto \frac{1}{\sqrt{t(1-t)}}$, and let $\tilde{h}$ denote its restriction to $\left]0, \frac{1}{2}\right]$. Show that the function $h$ is integrable on $]0,1[$ and that:
$$\int_0^1 h(t)\, dt = 2\int_0^{\frac{1}{2}} \tilde{h}(t)\, dt.$$