The Fundamental Theorem of Calculus (FTC) is like a bridge that connects two important ideas in calculus: differentiation and integration.

At first glance, these ideas might seem very different. But they actually work together really well!

Let’s break it down into two main parts:

1. Part 1: Understanding Antiderivatives

   This part says that if you have a continuous function, which we can call $f$, and you create a new function $F(x)$ by taking the integral of $f$ from a starting point $a$ to $x$, then $F(x)$ is an antiderivative of $f$.

   In simpler words, this means $F'(x) = f(x)$. So when you find the integral of a function, you’re actually reversing differentiation.

   It’s like a fun game where one idea leads you back to the other!

2. Part 2: Solving Definite Integrals

   The second part of the FTC makes it easier to calculate definite integrals using antiderivatives.

   If you want to find the integral of a function from $a$ to $b$, you can simply compute $F(b) - F(a)$. Here, $F$ is any antiderivative of $f$.

   This way, figuring out areas under curves becomes much simpler!

In my experience, learning how the FTC connects these two ideas helped me see calculus as a connected system instead of just a bunch of rules.

It made me appreciate math more, showing how everything is linked in the world of functions. Plus, it’s super helpful for solving problems in both differentiation and integration, making it a big deal in Year 12 calculus!