Can you give an example of just you are doing?
Suppose for example,
its jump points can be enumerated. Now what?
Let x1, x2,... be an enumeration of the jump points. Show that each jump is associated with a subinterval of [f(a), f(b)]. What are the endpoints of the ith jump subinterval.
Show all jump subintervals are either disjoint or at most share an endpoint.
Let [a1, b1], [a2, b2], ...[an, bn]be the first n jump intervals. We may relabel them so that a1<b1<a2<b2<...bn. So the sum of the lengths of the first n – subintervals is (b1-a1)+(b2-a2)+...+(bn-an)<=(a2-a1)+(a3-a2)+...+(f(b)-an)
finish the proof from here.