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Let f be a contiuous function on [a,b]. ...

Let `f` be a contiuous function on `[a,b]`. If `F(x)=(int_(a)^(x)f(t)dt-int_(x)^(b)f(t)dt)(2x-(a+b))`,
then prove that there exist some `c epsilon(a,b)` such that `int_(a)^(c)f(t)dt-int_(c)^(b)f(t)dt=f(c)(a+b-2c)`

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