Mathematics
The Fundamental Theorem of Calculus and Its Consequences
Quick fact
The Fundamental Theorem of Calculus has two parts: one says that the derivative of an integral (with a variable upper limit) gives back the original function; the other says that a definite integral can be evaluated by subtracting the antiderivative at the endpoints. This turns computing areas into finding antiderivatives.
Why this is interesting
You've probably heard that differentiation and integration are opposites—but have you ever wondered why that's true? This surprising link is the Fundamental Theorem of Calculus, and it's the secret behind almost everything calculus can do.