If int0^x[x]dx=int0^([x])xdx , then pro...

If `int_0^x[x]dx=int_0^([x])xdx ,` then prove that either `x` is purely fractional or `x` is such that `{x}=1/2(w h e r e[dot]a n d{dot}` denote the greatest integer and fractional part, respectively).

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