
At this point we have three “different” integrals.

At this point we have three different “integrals.” Let’s see if we can sort out the differences.

### Indefinite integrals

An indefinite integral, also called an antiderivative computes classes of functions: Here there are no limits of integration, and your answer will have a “$+C$” at the end. Pay attention to the notation:

Where $F'(x) = f(x)$.
Two students, say Devyn and Riley, are working with the following indefinite integral: Devyn computes the integral as and Riley computes the integral as Which student is correct?
Devyn is correct Riley is correct Both students are correct Neither student is correct

### Accumulation functions

An accumulation function, also called an area function computes accumulated area: This is a function of $x$ whose derivative is $f$, with the additional property that $F(a)=0$. Pay attention to the notation:

Where $F'(x) = f(x)$.
True or false: There exists a function $f$ such that
true false

### Definite integrals

A definite integral computes signed area: Here we always have limits of integration, both of which are numbers. Moreover, definite integrals have definite values, the signed area between $f$ and the $x$-axis. Pay attention to the notation:

Where $F'(x) = f(x)$.