Final answer:
The first part of the Fundamental Theorem of Calculus states that the definite integral of a continuous function from a to b is equal to the antiderivative of the function evaluated at b minus the antiderivative evaluated at a.
Step-by-step explanation:
The first part of the Fundamental Theorem of Calculus states that if f is continuous on the closed interval [a, b] and F is an antiderivative of f on [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a).
In other words, this theorem relates the concept of integration to finding the antiderivative of a function. It allows us to calculate the area under a curve by evaluating the antiderivative of the function at the upper and lower limits of integration.
For example, if f(x) = 2x on the interval [0, 3], we can find the area under the curve by finding an antiderivative of f(x), such as F(x) = x^2, and evaluating F(3) - F(0) = 9 - 0 = 9.