The author seems not to be aware of Bachelier. But it is inconvenient that the mathematical object of Brownian motion was first developed in the context of option pricing.I think Einstein pipped you at the post
http://stat.math.uregina.ca/~kozdron/Re ... and_BM.pdf
I think the proper line is “Thank you sir! May I have another?”Yes. Yes, I do.The main thing is have you understood where the integral comes from and how that integration by parts was achieved?