What is the analytical solution of the one dimensional Poisson equation?

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I have shown that by Lax-Milgram theorem that the following equation has unique solution.

$$ -u''+u=f~~in~~ \Omega=(0,1) $$ and boundary conditions are $u(0)=u(1)$ and $u'(0)=u'(1)$.

This is a one dimensional problem and I am trying to write its analytical solution. I am little confused in writing the particular solution of this problem that satisfies its boundary conditions.

Can anyone please help me with this?