The Fundamental Theorem of Calculus (FTC) is super important in math for a few key reasons:

1. Link Between Derivatives and Integrals: The first part of the FTC shows us that finding a derivative and calculating an integral are like opposite actions. If you can find a derivative, you can also figure out integrals!

2. Real-Life Uses: This theorem helps us calculate definite integrals, which are very useful in real life. For example, it helps us find areas and solve problems in physics.

3. Easier Calculations: The second part of the FTC tells us that if $F$ is an antiderivative of $f$, then you can find the integral from $a$ to $b$ using the formula $\int_a^b f(x) \,dx = F(b) - F(a)$. This makes calculating complex integrals much simpler!

Overall, the FTC is a key idea in advanced calculus and helps anyone interested in math understand more complex ideas.