When we need to reclassify a raster, we sometimes need to have a better control over what is included or not in an interval. Reclassifying tools in ArcGIS all work on the following proposition:
"Where overlapping occurs, the higher end of the lower input range is inclusive, and the lower end of the higher input range is exclusive."
The are some cases where this is not what is needed. Therefore we should have a tool that gives us complete control on how the interval end values are treated.