I had a question about Simpson's Rule for estimation of area under a curve and a problem that I just can't seem to grasp.

Recently my Calculus teacher had us evaluate/estimate(using Simpson's rule) the area from 0 to 2π of cosine(x) over n=6 (6 intervals). When the rule is followed exactly, the value of the area is 0, but it just doesn't stand as right to me.

In the problem what I did was take the absolute value of each section, but my Calculus teacher marked it wrong and said that the area is above the curve on sections where cosine(x) is negative (from 1π/2 to 3π/2) and thus the numbers will cancel each other out. My answer came out to something ~6.9ish I think.

Did I evaluate correctly or can areas really be "negative" (it just doesn't sit as logically right with me)?