Let \( n \) be a positive integer. Define \( f(x)=\min (|x-1|,|x-2|...

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Let \( n \) be a positive integer. Define \( f(x)=\min (|x-1|,|x-2|, \ldots .|x-n|) \). If
\( \mathrm{P} \) \( \int_{0}^{n+1} f(x) d x=2 \), then find the value of \( n \).

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