When writing the integral sign $\int$, how does one know what integral is being discussed? We have the Lebesgue integral and the Riemann Integral. Generally, must the integral sign $\int$ refer to one or the other exclusively or does it depend on the integrand? Can someone provide intuition to this concept?
For example, in college-level Calculus courses, what integral is actually being used here?

If a function is continuous on some closed interval then the two integrals will agree, hence a distinction is not necessary. Otherwise I believe the context should be enough.
