Math Help - zero content

1. zero content

Let f:[a,b]-> R be an integrable function.
Show that the graph of f in R^2 has zero content.
(hint: given a partition P of [a,b], interpret Spf-spf as a sum of areas of rectangles that cover the graph of f. )
Not sure where to start, any help?

2. Hint:

$f$ integrable in $[a,b]$ iff for every $\epsilon>0$ there exists a partition $P$ of $[a,b]$ such that $U(P,f)-L(P,f)<\epsilon$.