# How does the first fundamental theorem of calculus guarantee the

How does the first fundamental theorem of calculus guarantee the existence of antiderivatives of functions?
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Paxton James
If $f$ is an arbitrary continuous funciton, then you can define a function $g$ via the integral and by the fundamental theorem, the derivative of $g$ is $f$. That is: $g$ is an antiderivative of $f$. That's all.