Areas between curves

We know that integration gives us the ability to find the area underneath a curve between two points. But now, suppose we want to find the area that lies between two graphs, as in the following screenshot:

Our region S, as we can see, lies between the curves f(x) and g(x) in between the two vertical lines x = a and x = b. Therefore, we can take an approximation of the area between the curves to be the following:

We can rewrite this as an integral, in the following form:

To visualize this better and create an intuition of what is happening, we have the following image: