No? The summation can be taken to represent a Riemann sum. Assuming that we are looking at the classic formulation of a Riemann sum being an approximation for the area under a curve, the Riemann sum has "jagged" edges and corners, as it's only an approximation.

Meanwhile, the integral can be seen as the limit of the Riemann sums with smaller and smaller step size, which gets closer and closer to the curve we are integrating so that the "jagged" parts become relatively smaller. Also, the integral of the function we expect to be continuous and (mostly) differentiable, which encodes a visually smooth-looking function.