The area under the ROC curve is a common index summarizing the information contained in the curve. When comparing two ROC curves, though, problems arise when interest does not lie in the entire range of false-positive rates (and hence the entire area). Numerical integration is suggested for evaluating the area under a portion of the ROC curve. Variance estimates are derived. The method is applicable for either continuous or rating scale binormal data, from independent or dependent samples. An example is presented which looks at rating scale data of computed tomographic scans of the head with and without concomitant use of clinical history. The areas under the two ROC curves over an a priori range of false-positive rates are examined, as well as the areas under the two curves at a specific point.