Let F(x)=2x-∫(x, 0) f(t)dt- 1, then the question becomes whether F(x) has zero in (0, 1).

And the derivative function of f (x) =2-f (x) and f(x).

The derivative function is monotonous, and F(x) can only have one zero.

∫F(0)=- 1, f (1) =1-∫ (1,0) f (t) dt >1-∫ (/) According to the property of continuous function, F(x) must have a zero point in (0, 1).

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