A definite integral is a mathematical concept that represents the signed area under the curve of a function over a specified interval. It is denoted by the symbol ∫, where the limits of integration are provided as lower and upper bounds.

The definite integral of a function f(x) from a to b is written as: ∫_{a}^{b} f(x) dx

Here's what the notation and terms represent:

The symbol ∫ represents the integral.

a and b are the lower and upper limits of integration, respectively.

f(x) is the integrand, representing the function being integrated.

dx indicates the variable of integration (in this case, x).

The definite integral gives the signed area between the curve of the function and the x-axis over the specified interval [a, b]. The "signed" area means that areas above the x-axis contribute positively, and areas below the x-axis contribute negatively.

The fundamental theorem of calculus establishes a connection between definite integrals and antiderivatives (indefinite integrals). It states that if F(x) is an antiderivative of f(x), then: ∫_{a}^{b} f(x) dx = F(b) - F(a)

In practical terms, definite integrals are used in various fields such as physics, engineering, economics, and many other sciences to calculate quantities like displacement, area, volume, and more. The process of finding definite integrals involves techniques like the Riemann sum, the Fundamental Theorem of Calculus, and integration rules.