HMMT 2005 K8

Calculus
Answer

If $f$ is a continuous real function such that $f(x-1)+f(x+1) \geq x+f(x)$ for all $x$ , what is the minimum possible value of $\int_{1}^{2005} f(x) d x$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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2010012

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