Second Fundamental Theorem of Calculus

The second fundamental theorem of calculus holds for  a continuous function on an open interval  and  any point in , and states that if  is defined by the integral (antiderivative)

then

at each point in , where  is the derivative of .

REFERENCES:

Anton, H. "The Second Fundamental Theorem of Calculus." §5.10 in Calculus: A New Horizon, 6th ed. New York: Wiley, pp. 345-348, 1999.

Apostol, T. M. "Primitive Functions and the Second Fundamental Theorem of Calculus." §5.3 in Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, pp. 205-207, 1967.