I am studying for a final and have been solving extra problems in Spivak's Calculus. However, I am not sure how to write out the proof for a star problem in Chapter 14: Fundamental Theorem of Calculus.
Use the Fundamental Theorem of Calculus and Darboux's Theorem to give a proof of the Intermediate Value Theorem.
I think I have the idea, but I can't seem to formulate it into a rigorous formal proof. Basically, what I have in mind is letting $F$ be a function such that $F'=f$, and applying Darboux's thoerem on $F$. Then by FTC, we have the IVT??