Euler Lagrange equation $-u''=f(u)$

Question

Let $I\subseteq \mathbb R$ be an interval, $L=L(u,u',x)\in C^1(\mathbb R^3,\mathbb R)$ and $F[u]=\int_I L(u,u',x)dx$ for $u\in C^2(\mathbb R)$. Then the Euler Lagrange equation for the function $F$ is $-[\partial u' L(u,u',x)]'+\partial u L(u,u',x)=0$.
Now let $f\in C(\mathbb R)$. Determine a functional $F$ of the above form so that the ODE $-u''=f(u)$ is the Euler-Lagrange equation for $F$. Does anyone has a hint how to start here? I think I have to determine $L$.