The Fundamental Theorem of Calculus is really cool!

It shows how two important math ideas—derivatives and integrals—are like two sides of the same coin. Here’s a simple breakdown:

1. First Part: If you have a smooth function called $f(x)$, and you calculate its integral from point $a$ to point $b$, you find the area under the curve. In math terms, we say it like this: $F(b) - F(a) = \int_a^b f(x) \, dx$

2. Second Part: This part tells us that if we take the area we just found and find its derivative, we get back to the original function $f(x)$: $F'(x) = f(x)$

So, basically, if you integrate a function and then differentiate the result, you end up right back where you began! It's a pretty amazing connection.