Example 1

Tag 08BY, permanent. Cite it as [Bourbaki, Tag 08BY].

Functions of a Real Variable, chapter IV, § 1. EXISTENCE THEOREMS

For a differential equation of the form $x' = g(t)$ , where $g$ is regulated on $I$ , every integral $u$ is clearly defined on all of $I$ . One should note that $u$ can be bounded on $I$ without $g(t)$ being so.

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

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