Hi I recently read one that the domain of an accumulation function is always an open interval this does not quite make sense to me for example why can't the domain be a closed interval some help would be appreciated as I've been confused for a while
2026-04-25 09:39:30.1777109970
Calculus and integration
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Let $f:I \to \mathbb R$ be a integrable function ,where $I$ is an interval in $ \mathbb R$, then a function $F$ of the form
$$F(x) = \int_\xi^x f(t)dt$$
is called an accumulation function, where $\xi \in I$ and $x \in I$.
The interval $I$ has not to be open, $I$ can be an interval of any form $(a,b), (a, \infty), [a,b]$, ...... .