Since when $f(x)$ is undefined at $x=c$ and $a \leq c \leq b$
$\int_{a}^{b}f(x)dx$
is undefined as it takes the definite integral over an undefined region of the function. Or in another sense, since all definite integrals that cover an undefined portion of $f(x)$ are undefined.
And since
$\int_{a}^{a}f(x)dx=0$
is considered true (at least to my understanding) for any value, $a$, and any function, $f(x)$. Does that make
$\int_{c}^{c}f(x)dx=0$
or
$\int_{c}^{c}f(x)dx$ undefined
When $f(x)$ is undefined at $x=c$?