Nope. Integral is the sum of infinitesimal values, not zeroes. If you dig into definition of Riemann integral, then you'll see that the are no zeroes in the sum

Nope. Integral is the sum of infinitesimal values, not zeroes. If you dig into definition of Riemann integral, then you'll see that the are no zeroes in the sum at any step. Except for zeroes of function being integrated, of course. For example Riemann integral is just limit of sums built on tagged partitions of a closed interval with largest sub-interval approaches zero. But no single sub-interval is equal to zero, their lengths just approach zero while being strictly positive values. Calculus does not divide by zero, calculus explores what happens when we move to zero as close as we can and even closer.