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Yes, but only in some cases and they are special types of integrals: Lebesgue integrals.
Flux integrals, surface integrals, and line integrals!
Gottfried Wilhelm Leibniz is credited with defining the standard notation for integrals.
There are two types of integrals: definite and indefinite. Indefinite integrals describe a family of functions that differ by the addition of a constant. Definite integrals do away with the constant and evaluate the function from a lower bound to an upper bound.
People often divide Calculus into integral and differential calculus. In introductory calculus classes, differential calculus usually involves learning about derivatives, rates of change, max and min and optimization problems and many other topics that use differentiation. Integral calculus deals with antiderivatives or integrals. There are definite and indefinite integrals. These are used in calculating areas under or between curves. They are also used for volumes and length of curves and many other things that involve sums or integrals. There are thousands and thousand of applications of both integral and differential calculus.