I'm reading a book on PDE's and they introduce ''Green's formula'' in a rather (to me) abrupt way. It is used to derive that for a steady state heat PDE $u(x)$ is given by: $u(x)=\int_{a}^b f(x_0)G(x,x_0) dx_0$.
$$ \int_{a}^{b} [uL(v)-vL(u)]dx=p\left( u\frac{du}{dx}-v\frac{du}{dx}\right)\big|_{a}^{b}$$
Can someone explain me where this Green's formula comes from? ($L$ is the Sturm Liouville operator)