Is Grönwall's Lemma true only for non-negative functions?

For instance, in this article of Wikipédia a statement is made for Differential form of the Grönwall's Lema for a $$\beta, u:I:=[a,b]\subset \mathbb{R} \longrightarrow \mathbb{R}$$ continuous functions and $$u$$ differentiable in the interior $$I^{\circ}$$ of $$I$$. That is, $$u$$ and $$\beta$$ are not necessarily non-negatives. Where, $$u'(t) \leq \beta(t)u(t) , \; \forall \; t \in I^{\circ}\Rightarrow u(t) \leq u(a)e^{\int_{a}^{t}\beta(s)}ds, \; \forall \; t \in I.$$

The versions of the Grönwall's Lema that I know of require that the functions be non-negative. Is that what's on Wikipedia right? If so, is there a reference that contains this result?

In the statement of the article, quoted above, an observation is made: There are no assumptions on the signs of the functions $$\beta$$ and $$u$$.

I did not see error in the proof presented there.