What is the difference between a definite integral and an indefinite integral?

A definite integral is actually a numerical value, which the represents the area under a graph between two points. For example, if you integrated f(x) between two values (lets call them a and b), the answer will be the area under the graph between x=a and x=b.On the other hand, an indefinite integral is an expression that can differentiate to f(x). So when asked to find the indefinite integral F(x), you are simply being asked what function F(x) differentiates to f(x).