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 athirdtrapezium 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