As Sir Isaac Newton an Leipniz and others originally conceived of the Calculus, "Calculus" is the mathematics of infinitessimals, or things that are infinitely small. The term "integrate" means to bring pieces together into one whole. An integration in Calculus is a summation, an adding together of infinitessimals.
The integral sign,? , is actually a large "S" standing for a particular mathematical type of addition or summation. How do you add up things that are infinitely small?
Well, that is accomplished by the Mathematics of Calculus, specifically, integration.
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