To find the area under a curve using definite integrals in calculus, you can follow these easy steps:

1. Define the Function and Interval: First, you need to pick the function, which we’ll call $f(x)$. Then, decide the interval, which is the range you want to look at, shown as $[a, b]$.

2. Set Up the Integral: The area, which we'll call $A$, can be written as a definite integral. This is a special way to show the area:

   $$A = \int_{a}^{b} f(x) \, dx$$

3. Evaluate the Integral: To find the area, we use something called antiderivatives. This relates to the Fundamental Theorem of Calculus. It tells us:

   $$A = F(b) - F(a)$$

   Here, $F(x)$ is the antiderivative of $f(x)$.

4. Calculate the Result: Now, plug in the numbers for the limits into the antiderivative to get the area.

Example: Let’s say our function is $f(x) = x^2$ and the interval is $[1, 3]$. First, we find the antiderivative:

$$F(x) = \frac{x^3}{3}$$

Next, we evaluate it:

$$A = \left[ \frac{3^3}{3} - \frac{1^3}{3} \right] = 8$$

So, the area under the curve from $x=1$ to $x=3$ is 8 square units.