Sixteen hundreds simultaneously and independantly by Issac Newton and Leibniz in Germany. For about a hundred years after, Britain was still incandescent with rage because we thought Leibniz had copied Newton. Interestingly, the Germans just ignored it and went on and for the next century they had thousands ofbrilliant scientists whilst we were still fuming. :)
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Integral calculus was invented in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz.
the example and solution of integral calculus
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.
Gottfried Leibniz is called the father of integral calculus.
The link has the answer to your question. http://www.sosmath.com/calculus/integ/integ03/integ03.html