Fundamental theorem of calculus: continuity and oriented endpoints

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

Fundamental theorem of calculus: continuity and oriented endpoints

With continuity on all R, differentiation of the accumulating integral recovers the integrand; an eligible antiderivative gives an oriented endpoint difference.

atlas-fundamental-theorem-calculus · canonical_mko

Prerequisite nodes

Real derivatives at a point and finite difference quotients
Signed polynomial definite integrals on finite intervals
Point values and continuity of real functions
Polynomial antiderivatives and the choice of constant
Differentiating polynomial sums, products, and compositions