It's a good start. Note that since you are using the right-side sum, and cos(x) is concave down and rising on that interval, the sum will be an upper estimate.

Use the left-side sum for a lower estimate.

Draw a few rectangles and the curve to see why this is true.

You can estimate the area with a single rectangle, of width pi/2 and height 1, but it won't be a very good estimate.

Also, my bad. I was thinking of sin(x) when I mentioned that the estimate was over- or under-. The reverse for cos(x), since it is decreasing on the interval.

And yes, you need to worry about the interval, since that was what was specified in the problem!!!

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