# Poisson Equation with Boundary Value Problem

I am trying to learn about solving boundary value problems, but I stuck when I came to finding BVP of $$1$$D Poisson equation on $$[0,1]$$: $$\begin{cases} \dfrac{\mathrm{d}^2}{\mathrm{d}x^2}u(x)=-g(x) \\ u(0)= a \\ u(1)= b \end{cases}$$ where $$g(x)=−6\pi \cos(3\pi x)+9\pi^2x \sin(3\pi x)$$ and $$a=b=0$$.

Should I get the integral of given $$g$$ two times and then plug in the $$u(0)$$ and $$u(1)$$ values to find out the values of the two integration constants $$c_1$$ and $$c_2$$? Or am I supposed to do something else? Also, how can I start solving it numerically by discretization for any $$h$$ value? Any hint or tip is appreciated.