Suppose I have to solve the following boundary value problem:
$-u''=f\quad\text{and}\quad u(0)=0,\ u(1)=0.\qquad \mbox{Where $f \colon [0,1] \to \mathbb{R}$.}$
In the solution to the exercise, the professor integrates as follows to solve the equation: $u(x)=-\int_{0}^{x}\int_{1}^{y}f(s)dsdy+c_{1}x+c_{2}$
Could someone explain to me why does he use these limits of integration specifically? Why from $1$ to $y$ then from $0$ to $x$?