As N goes to infinity, this effectively turns into a Riemann sum since we are sampling at points spaced with an infinitesimally small distance across the range of the integral and just multiplying the width of each gap by the function at that point.

As N goes to infinity, this effectively turns into a Riemann sum since we are sampling at points spaced with an infinitesimally small distance across the range of the integral and just multiplying the width of each gap by the function at that point.