Notation: Unknown integral range for general case

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If I don't know the range of values to integrate over, but want to provide a general notation to integrate over all $c$, how would I write this notation?

Would this work?

$$ \int_{c} f(c)dc $$

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What you have to put under your integral sign is the domain in which the variable $c$ belongs. For instance, if $f$ is defined on all the real numbers, you would write $$\int_{\mathbb{R}} f(c) dc$$

(note that it doesn't imply that your integral has a sense ; it can be divergent).