I could be mistaken, but if I recall correctly, I think it was Leibnitz who used that elongated S, which stands for "Sum" or Δ <--- delta, bearing in mind that, an integral is obtained by a Sum, like in a Riemann's summation, using the sum of the area segmentation by their Δy and Δx.
So, is a mnemonic notation for a sum, using the Latin letter S.