Riemann Sum Question: Is my Answer Correct?

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The discussion centers on a Riemann sum problem where the user questions the correctness of their textbook's answer. They express confusion over the use of 32 as the denominator for the endpoints, while they believe their calculation should involve a denominator of 12 based on their Δx value. The user acknowledges a mistake in their approach, particularly in not including function notation around their fractions. They seek clarification and assistance from others, indicating a desire to understand the Riemann sum process better. The conversation highlights common pitfalls in calculating Riemann sums and the importance of proper notation.
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Hello, just going through some Riemann sum problems before I hit integrals and I am like 99% sure that this answer from my text is wrong but I want to make sure. It's not really an important question so if you have better things to do, help the next guy :) But checking this over would be appreciated!

http://img178.imageshack.us/img178/875/incorrectyp5.jpg

I am trying to find an approximation of the integral using a Riemann sum.

Here is the question.

http://img216.imageshack.us/img216/2113/incorrect2jj8.jpg

Why are they using 32 as the denominators for their endpoints? I have the same numerators but my denominator is 12 since \Delta x=\frac{\pi}{6}. And for my first midpoint I would use half that.. \frac{\pi}{12}, and then add delta x again n times, right?
 
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It's sec(x/3).
 
Sigh, how dumb of me... thanks, arg!

If I had f()'s around my fractions I would have been fine, forgot about that. :( Thanks though, and sorry.
 
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