If I have an integral function, for instance $F(x)=\int_1^x \frac{1}{\sqrt{3-t}}\,dt$, surely the domain of the integrand is $(-\infty, 3)$ and then can I say that since $\lim_{x\to 3^-}F(x)=\int_1^{3} \frac{1}{\sqrt{3-t}}\,dt$ converges I can continuously extend the integral function in $x=3$ imposing that $F(3)=\lim_{x\to 3^-}F(x)\in \mathbb{R}$?
2026-03-29 10:12:17.1774779137
Extend continously an integral function
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