# Integration and continuity by Dimitris

Calculus Level 3

Let the function $$f$$ be twice differentiable on $$\mathbb R$$ and also continuous on $$\mathbb R$$, and that $$\displaystyle \int_0^\pi (f(x) + f''(x)) \sin x \, dx =\pi$$ and $$\displaystyle \lim_{x\to0}\dfrac{f(x)}{\sin x} = 1$$. Find $$f(\pi)$$.

 Notation: $$\mathbb R$$ denotes the set of real numbers.

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