When $f$ is continuous on $[a,b)$, the definite integral of f is
$$ \int_a^b f(x) dx. $$
When $g$ is continuous on $[a,b]$, the definite integral of g is
$$ \int_a^b g(x) dx $$
How can you explain the difference between those two? (as advanced calculus or analysis maybe)
Thanks for reading it.