Using rectangles as a tool in approximating areas is as old as the hills, but is brand new to many students and incomprehensible to some people. My position is that by using technological tools such as GeoGebra in a well-designed manner, topics such as this can clarified. This one (full file here) utilizes some features of GeoGebra that I personally just learned about. I hope to improve on it over time. Have fun.