You don't go from (1) to (2). You go from the first of your integrals to (2).

Picture it as the area under a curve and slide this say p units to the right.

The area doesn't change, the limits now go from p-h to p+h and the approximation becomes

.

Now put p-h = a, p+h = b, and solve for p and h in terms of a and b.