Explanation
\displaystyle \int f''(x) \sin x dx
\displaystyle = \sin x f'(x) - \int \cos x f'(x) dx
\displaystyle = \sin x f'(x) - \left[ \cos x f(x)+ \int \sin x f(x) dx \right]
\displaystyle \Rightarrow \int \left[ f(x)+f''(x) \right] \sin x dx= \sin x f'(x)dx- \cos x f(x)
\displaystyle \Rightarrow \int_0^\pi \left[ f(x)+f''(x) \right] \sin x dx=\left[ \sin x f'(x)dx- \cos x f(x) \right]_0^\pi
\Rightarrow 5= f(\pi)+f(0)
\Rightarrow f(0)=5-2=3
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