After going through all the painstaking proofs, I have finally come to this step:

If we denote z as , we can scale the above formula to the standard normal curve:

When we calculate the area under 2 points on the z-axis, say, A to B, we do :

But why is the integral given as:

What happens to the "npq" term?

Please help to alleviate my doubt if you can. Thanks!