Jogging Memory: Trapezium Rule Formula

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bill nye scienceguy!
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jog my memory, what's the formula for the trapezium rule again?
 
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Alternatively, try to think back at HOW the trapezoidal rule was constructed; i.e, what is the mathematical idea behind it?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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