Definite integrals provide numerical solutions to the area under a function for a given interval. For a function f(x) that is continuous over the interval [a, b], the integral of the function from a to b is equal to the limit, as n approaches infinity, to the Riemann sum over [a, b] from i = 1 to n: , where is a subinterval of [a, b] and is the midpoint within each subinterval. Over the interval [a, b], called the interval of integration, a is called the lower limit and b the upper limit. According to the first fundamental theorem of calculus, the integral of a function from a to b can be calculated by subtracting the antiderivative F(a) from the antiderivative F(b): .
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