What is the Fundamental Theorem of Calculus?

The Fundamental Theorem of Calculus connects the two main ideas in calculus: derivatives and integrals. It says that finding the area under a curve (an integral) and finding the rate of change (a derivative) are actually opposite processes. This means if you know how something changes (its derivative), you can find the total result (its integral), and vice versa. This connection is powerful because it allows complex problems to be solved more easily. The theorem acts as a bridge, showing how small changes add up to create a whole, and how a whole can be broken into changes.