Calculus is a branch of mathematics, developed from algebra and geometry, built on two major complementary ideas.
The first idea, called differential calculus, is about a vast generalization of the slope of a line. It is a theory about rates of change, defining differentiation. It permits velocity, acceleration, and the slope of a curve at a given point all to be discussed on a common conceptual basis.
The second idea, called integral calculus, is about a vast generalization of area. It is a theory about accumulation of small, even infinitesimal, quantities, defining integration.
Though originally motivated by area, it includes related concepts such as volume and even distance.
The two concepts differentiation and integration define inverse operations in a sense made precise by the fundamental theorem of calculus. Therefore, in teaching calculus either may in fact be given priority, but the usual educational approach (nowadays) is to introduce differential calculus first.