An integral is a fundamental concept in calculus that represents the accumulation of quantities, such as area under a curve. It helps in finding the total value when given a rate of change, which is the opposite of differentiation. Integrals can be classified into two main types: definite and indefinite. A definite integral calculates the total over a specific interval, while an indefinite integral represents a family of functions. In practical applications, integrals are used in various fields, including physics, engineering, and economics. For example, they can determine the total distance traveled over time when given a speed function. The process of calculating integrals often involves techniques such as substitution and integration by parts, making it a versatile tool in mathematical analysis.