It sounds like you might be referring to the Fundamental Theorem of Calculus (FTC), where we compute definite integrals by evaluating the antiderivative at the upper and lower limits of integration, and then subtracting the values.

For example, given a function $f(x)$ and its antiderivative $F(x)$, the definite integral from $a$ to $b$ is:

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

In some cases, like with improper integrals or integrals involving limits (i.e., where one or both of the limits are infinite), you may calculate the integral by first evaluating the antiderivative at a specific point (like $t$) and then subtracting the corresponding value at the lower limit (or zero). This is often seen when evaluating limits like:

$\lim_{t \to 0^+} \int_0^t f(x) \, dx$

Would you like to dive deeper into a specific example or type of integral using this method? Feel free to share the integral you're working on.

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Related Questions:

1. Can you explain the Fundamental Theorem of Calculus in more detail?
2. How do we evaluate integrals with limits approaching zero or infinity?
3. What is an improper integral, and how do you compute it?
4. How can we use substitution in definite integrals?
5. Can you explain how to handle definite integrals with discontinuities?

Tip: Remember that the antiderivative is key to using the Fundamental Theorem of Calculus—always check if you can simplify your function first, to make finding the antiderivative easier.