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Let \(f\) be a function defined on an interval \(I\). According to the definition, \(F\) is an antiderivative of \(f\) on \(I\) if and only if:
\(f\) is differentiable and \(f'(x) = F(x)\) for all \(x \in I\).
\(F\) is differentiable and \(F'(x) = f(x)\) for all \(x \in I\).
\(F(x) = f(x) + C\) where \(C\) is a real constant.
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