# 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.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Fundamental theorem of calculus: continuity and oriented endpoints](https://ocme.evemisslab.com/en/atlas/atlas-fundamental-theorem-calculus/)

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

[Fundamental theorem of calculus: continuity and oriented endpoints](https://ocme.evemisslab.com/en/mko/mko-fundamental-theorem-calculus/)

## Prerequisite nodes


- [Real derivatives at a point and finite difference quotients](https://ocme.evemisslab.com/en/atlas/atlas-derivative/)
- [Signed polynomial definite integrals on finite intervals](https://ocme.evemisslab.com/en/atlas/atlas-definite-integral/)
- [Point values and continuity of real functions](https://ocme.evemisslab.com/en/atlas/atlas-continuity/)
- [Polynomial antiderivatives and the choice of constant](https://ocme.evemisslab.com/en/atlas/atlas-antiderivative/)
- [Differentiating polynomial sums, products, and compositions](https://ocme.evemisslab.com/en/atlas/atlas-derivative-rules/)