Definite integrals are a way to understand the area below a curve, but this can be tough for students to grasp. The curves we look at can have strange shapes or can be broken, making it hard to figure out the area.

1. Understanding the Concept:

   • To find the area under a curve represented by $y=f(x)$ from $x=a$ to $x=b$, we break this section into smaller parts. We create rectangles, where the height of each rectangle is based on the curve's values. This method seems easy, but doing it correctly involves careful calculations.

2. The Limit Process:

   • The definite integral is shown as $\int_a^b f(x) \, dx$. This represents the total area of these rectangles as their width gets really tiny, almost to zero. This idea can be hard to understand and work with.

3. Practice Makes Perfect:

   • Many students find it difficult to learn how to calculate these integrals. However, if they practice with different functions and use methods like Riemann sums, they can get better at it and find it easier to understand.