Yes, the area of a single trapezium is given by . If you add one more trapezium, from to you get which reduces to .
If you use a third trapezium you get
which reduces to .
Do you see the point? Everytime you add one more trapezium, from n to n+1, you add a new " " making the coefficient of 2.
That is, you have , all but the first and last terms multiplied by 2. And that is always multiplied by .
You can write that using the notation as
If you are integrating f(x) from x= a to x= b and want to use n intervals, then