Formulas for composite/multiple-segment trapezoidal rule (for approximating the value of an integral) don't seem to agree?

It could be a difference in how N is defined. Let's look at them. First of all, let's derive the actual trapezoidal rule.
If we have points from x_0, x_1, ..., x_N dividing the region up into N intervals (x_0 = a and x_N = b), then the area of the corresponding trapezoids is
(h/2) (f(x_0) + f(x_1)) + (h/2)[f(x_1) + f(x_2)] + ... + (h/2) [f(x_N-1) + f(x_N)] where h = the spacing between x values. All of the interior values x_1, x_2, ..., x_N-1 appear twice, so that gives
(h/2) [ f(x_0) + f(x_N) ] + h sum(i = 1 to N-1) f(x_i). The first term uses the endpoints, the second term is a sum over all the interior points between those endpoints.

The first one has x values from x_2 to x_(N-1), plus a and b. So that looks like the x values are numbered from 1 to N, with x_1 = a and x_N = b, and there are only N-1 intervals. That seems inconsistent with the text as written. If there are four intervals then according to this numbering scheme N = 5. If there are two intervals then N = 3.

The second one numbers the interior points from 2 to N, so the endpoints are a = x_1 and b = x_(N+1). There are N+1 points dividing it up into N intervals.

The third one numbers the interior points from 1 to (N-1), so there are (N-1) interior points defining N intervals, with x_0 = a and x_N = b.

Summary: First formula uses N for the number of points, and numbers those points from 1 to N.
Second formula uses N for the number of intervals, and numbers the points from 1 to N+1.
Third formula uses N for the number of intervals and numbers the points from 0 to N (that's the notation I chose, but I could have used either of the other two).

They're equivalent, just have different definitions for the variables.