2014 Putnam B2

Suppose that $f$ is a function on the interval $[1,3]$ such that $-1 \leq f(x) \leq 1$ for all $x$ and $\int_1^3 f(x)\,dx = 0$. How large can $\int_1^3 \frac{f(x)}{x}\,dx$ be?

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假设 $f$ 是区间 $[1,3]$ 上的函数，对于所有 $x$ 且 $\int_1^3 f(x)\,dx = 0$，$-1 \leq f(x) \leq 1$。 $\int_1^3 \frac{f(x)}{x}\,dx$ 可以有多大？

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