The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly struggle with the fundamental theorem, especially its second part. They have trouble both with its meaning and how to use it, and this confusion is reinforced by textbooks that often present it as an exercise in symbol manipulation. The standard presentation of the second FTC leads to a misconception that it is a statement about computing derivatives, when in fact it is a statement about constructing antiderivatives. In this article, the author considers an alternate way of presenting the second part of the FTC that takes the emphasis away from symbol manipulation to compute derivatives and focuses on the more subtle meaning of the theorem: the existence of antiderivatives.