Remark 2

Tag 087L, permanent. Cite it as [Bourbaki, Tag 087L].

Functions of a Real Variable, chapter II, § 1. PRIMITIVES AND INTEGRALS

For an arbitrary function $h$ defined on I, with values in E, the element $h(x) - h(x_0)$ is also written as $h(t)\Big|_{x_0}^x$ ; with this notation one sees that if $g$ is any primitive of a regulated function $f$ on I, one has

\int_{x_0}^x f(t) dt = g(t)\Big|_{x_0}^x.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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