What happens when one integrates a function that includes the absolute magnitude of x?

Such as the integral of exp[-c*(abs(x)]

I've seen some examples where the integral is taken only from 0 to the upper limit, and doubled, suggesting a symmetric function about the y axis I suppose.

Also would I be correct in thinking that abs(x) is not a "real" mathematical function like squaring etc..., if this is correct my question is how do you get it into an integral form that is equivalent.

Thanks, help would be vastly appreciated anyone.

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