Integral calculus, also known as integration, is one of the two branches of calculus, with the other being differentiation. Differentiation describes how the value of a function changes with respect to its variables. Integration is the inverse, in that it gives the exact summation of a function between two values. Integral calculus provides an exact means of calculating the area under the curve of a mathematical function. Integration has a wide range of applications in physics and engineering.The two pioneers of calculus were the 17th century scientists Isaac Newton and GottfriedLeibniz. The mathematical notation used today is based on the work of Leibniz. Although undoubtedly a great scientist, Newton had a reputation for being very competitive and vindictive, and he was unwilling to share the credit with his German contemporary. Newton used his considerable influence at the Royal Society in London to directly and indirectly accuse Leibniz of plagiarism. The validity of these accusations has never been verified, but the controversy destroyed Leibniz's reputation.