The Fundamental Theorem of Calculus can seem hard to understand at first, but it really has two main ideas that connect different math concepts.

Part 1: This part shows how differentiation and integration are related.

• If you have a function ( f ) and its antiderivative ( F ) on an interval from ( a ) to ( b ), then you can find the area under the curve of ( f ) between these two points.

• You do this using the formula: $\int_a^b f(x) \, dx = F(b) - F(a)$.

Some students find it tough to figure out antiderivatives, and that can feel a little overwhelming.

Part 2: This part explains that if ( f ) is a continuous function, then you can define a new function ( F(x) ) using integration.

• The equation looks like this: $F(x) = \int_a^x f(t) \, dt$.

• And then, when you find the derivative of ( F ), it equals ( f(x) ): $F'(x) = f(x)$.

To make these ideas easier to understand, it’s important to practice regularly. Getting help from a tutor or using other resources can also clarify these concepts and boost your confidence in calculus.