Let f be a continuous function on [a , b...

Let `f` be a continuous function on `[a , b]dot` If `F(x)=(int_a^xf(t)dt-int_x^bf(t)dt)(2x-(a+b)),` then prove that there exist some `c in (a , b)` such that `int_a^cf(t)dt-int_c^bf(t)dt=f(c)(a+b-2c)dot`

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