Possible Duplicate:
Lebesgue measure on Riemann integrable function in $\mathbb{R}^2$
Is the Lebesgue integral of a positive real function of a real variable equivalent to the Lebesgue measure of the set (in $\mathbb{R}^2$) of all the points between the interval of integration and the graph of the function?
I'm asking this because all the different definitions of "length", "area", "volume", "measure" I was exposed to (Euclidean geometry, path length, measure of a set, integral, scalar product, ...) seem to be different from one another and I would like to see what are the points in common