Integral of normal distribution

I thought i made a discovery that the Sigmoid function was the integral of the Normal Distribution whose integral according to normal calculus has no solution.

Unfortunately i was beaten by a few years
https://www.sciencedirect.com/science/article/abs/pii/0096300395001905

This is my effort in basic on the caprice amstrad emulator showing a plot of the normal distribution integral and the sigmoid function overlapping exactly. 
This is a hot peice of maths for a good mathematician like Terence Tao or Grant Sanderson, 3 blue one brown youtube to prove. 
 

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