Drawing a function which contains an Integral

Hello,
I am trying to draw this function:


Do I need to find the integral at a set of points and then draw the function or is there a way to define the function as an integral in TF1, so it can be drawn easily?
Thank you.

The denominator can be modified to b 1- the integral from 0 till t if this makes it easier.

Wikipedia → Normal distribution
Wolfram MathWorld → Normal Distribution

TMath::Gaus
ROOT::Math::gaussian_pdf
ROOT::Math::normal_pdf

TMath::Erf
ROOT::Math::erf

TMath::Erfc
ROOT::Math::erfc

ROOT::Math::normal_cdf