Given a function f that is continuous on an interval , we can integrate the function from c to x such that and .
Now let on represent the resultant general but particular anti-derivative of f. Now, represents the sum of area under the curve f from c to x. It’ll be positive if and negative if . For example, as you increase x, the ending point of the area extends to the right (positive x-axis). As you decrease it, it shrinks to the left (negative x-axis); at some point, it becomes negative and extends to the left negatively.
Furthermore, where and is a difference of area under the curve f starting from c to each p and q. In addition, consider . dF is a small area under the curve f whose height is f and whose width is dx. Thus, . Then as given.