An integral as seen above means that the function f(x) needs to be bounded on the interval [a, b] (both real numbers), and the interval also must be bounded. But an improper integral is one in which the function f(x) becomes unbounded (called a type I improper integral) or the interval [a, b] becomes unbounded (a = -∞ or b = +∞, which is called a type II improper integral).