To solve problems with the Fundamental Theorem of Calculus, AS-Level students should follow these steps:

1. Understand the Theorem: This theorem shows how differentiation (finding a rate of change) and integration (finding the area under a curve) are connected.

   It says that if $F$ is an antiderivative of $f$ in the range $[a,b]$, then:

   $\int_a^b f(x) \, dx = F(b) - F(a)$

2. Identify Functions: First, find the function $f(x)$ that you need to integrate, and then determine its antiderivative $F(x)$.

3. Substitute Limits: After finding $F(x)$, plug in the upper limit ($b$) and the lower limit ($a$) to calculate the definite integral.

Example: Let’s say our function is $f(x) = 3x^2$. We will find:

1. The antiderivative $F(x) = x^3$.

2. Now, evaluate the integral:

   $\int_1^2 3x^2 \, dx = F(2) - F(1) = 8 - 1 = 7.$

Practice with different functions to get more comfortable with these steps!