Definite integral from a to b of sqrt(x) (one-valued vs. multi-valued)

Given that 0<a<b, the definite integral from a to b of sqrt(x) yields
a positive value c. That's true if we treat sqrt(x) as a one-valued
function. Now, I've sometimes seen the graph of sqrt(x) drawn as a
multi-valued function and it looks like a "C". In such circumstances,
is it correct to say that said definite integral yields +/- c? Does it
make sense to use multi-valued functions in an integral, or must one
necessarily use one-valued functions?

Thanks for your feedback.
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