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=[itex]\frac{arctan x}{x}[/itex] for x different from 0

= 1 for x equal to 0

F(x) is a definite integral from 0 to x, but I couldn't find the code for it, so just assume it is from 0 to x in the equation below.

F(X) = [itex]\int f(t) dt[/itex]

Now, the task is to prove that F(-x) = -F(x).

This means we need to prove:

[itex]\int f(t) dt[/itex] : definite from 0 to -x

=

-[itex]\int f(t) dt[/itex] : definite from 0 to x

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We have tried some basic manipulation of integrals, but came nowhere.

If anyone can give a hint of how to prove this, or tell us if we have understood the problem wrong, we would be most grateful.

Thanks.