Trapezoidal Rule/ Having trouble understanding what is k?! QUESTION:
I know of the more understanding formula for the trapezoidal rule. However, I came across this new form in a book i'm reading. Can someone tell me how I'm suppose to enter the respected values into this new form. Really would like to understand what is going on.

I'm assuming that the first part (b-a)/n will come to 1 so we can disregard it. 
Next I'm assuming that [f(a) + f(b)]/2 will be set up like (f(-2)+f(5))/2 which is about 3.667544
The summation part is confusing and I'm not even for sure if i'm correct above. I'm coming out with an answer around 13.334698. Which it should be around 17.017422. Any guidance is appreciated. 

The sum gives you the following values (the first value is the value of $x$ that is put into the function at each step, so you can verify)::


*

*$−1.,1.41421356237309505$

*$0.,1.$

*$1.,1.41421356237309505$

*$2.,2.2360679774997897$

*$3.,3.16227766016837933$

*$4.,4.12310562561766055$


The sum of those values is: $13.3498783880320197$.
The result of $\displaystyle ~\frac{f(a)+f(b)}{2} = 3.66754374554628726$
The final result is the sum of those two and is $17.0174221335783069$.
The actual result from the integral is $16.8617$.
Here is a Trapezoidal calculator showing the results.
