Ito’s Integral: Why Riemann-Stieltjes approach does not work, and how does Ito’s approach work?

Explains visually the Riemann-Stieltjes approach, and why it does not work when the integrator is a Brownian motion. It then explains how a new approach, based on approximation of the integrand by simple functions works, and proves that the Ito’s integral of the step function converges, and is uniquely defined.