What's this integral definition?

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I've seen the integral definition:

$$\int_a^b f(x) \, dx = F(b)-F(a) = \lim_{x\rightarrow b-}F(b) - \lim_{x\rightarrow a_+}F(a)$$

Anyone know what's this "limit version" called?

I know it applies to indefinite integrals.