Prove that if f(x) = integral from 0 to x of f(t) dt then f = 0

Prove that if f(x) = integral from 0 to x of f(t) dt then f = 0

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if \[f(x) = \int\limits_{0}^{x} f(t) dt \]
then f = 0

This is not a true statement.

Michael Spivak claims it is

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