Fläche (Ober- und Untersummen)
In antiquity, already Archimedes was calculating the area beneath a parabola by dividing the area into thin strips (see Streifenmethode).
Here is a link to an interactive German geogebra book by Hans-Jürgen Elschenbroich: Der Integrator
area function - Flächenfunktion
anti-derivative - Stammfunktion
links
CIMT - MEP on volumes of revolution
CIMT - MEP - partial fractions
CIMT - MEP - integration using trig functions an partial fractions