Given: $f^{\prime\prime}(x)$ is continuous, $f(\pi) = 0$, and $\int_0^\pi (f(x)+f^{\prime\prime}(x))\sin(x) \, dx = 2.$
Find: $f(0)$.
I know integration by parts etc, but I do not know which particular concept(s) I'm supposed to apply for this one. Or is there a specific theorem I am missing?