Understanding Subintervals in Calculus

Subintervals are smaller intervals that are contained within a larger interval. For example, if we have the interval [a, b], then any interval of the form [c, d] where c is between a and b, and d is between b and a, is a subinterval of [a, b].

Here's an example to illustrate this:

Suppose we have the interval [0, 10]. The subintervals of this interval are:

* [0, 2]
* [2, 4]
* [4, 6]
* [6, 8]
* [8, 10]

Each of these subintervals is contained within the larger interval [0, 10], and they all have the same endpoints as the larger interval.

Subintervals are important in calculus because they allow us to study functions on smaller intervals, which can sometimes be easier to work with than the entire interval. For example, if we have a function that is difficult to integrate over the entire interval [0, 10], we might try breaking it down into smaller subintervals and integrating each one separately. This can make the integration process easier and more manageable.