$$ \int_a^bf(x)dx $$
\int: integral sign (limit of sum)
f(x): integrand—the one being integrated
a and b: the limits of integration
dx: infinitesimal | Linearization and Differentials
A definite integral is a number, whereas an indefinite integral is a family of functions.
Upper and lower bond integration, yields out the accumulation of change. (Definite integral of one’s function, yields out the original function’s total net change.)
The Fundamental Theorem of Calculus
Mean Value Theorem for Integrals
Displacement and Distance with Integration