Gottfried Wilhelm Leibniz developed Leibniz notation. In Leibniz notation, differentiation looks like a fraction dy/dx and integration looks like a long S, which was used in Germany at the time, to denote "sum" (as in the sum of infinitely thin rectangles used in definite integration).
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That would be Leibniz.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
Calculus, both differential and integral.
One directly undoes the process of the other.
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.