Integral calculus, area under curve. This diagram demonstrates how the area under a graphed curve relates to the key mathematical concept of integral calculus. This area of mathematics involves applying a process called integration to a mathematical function to determine areas and volumes. Here, the mathematical function is the red line f(x). The area 'S' under the curve is the integral of f(x) between the limits 'a' and 'b', which is the integrated function with x=b, minus the integrated function with x=a. There are numerous applications of this concept, which was developed as a practical method by Newton and Leibniz in the 17th century.