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 firstnjump intervals. We may relabel them so that a1<b1<a2<b2<...bn. So the sum of the lengths of the firstn– subintervals is (b1-a1)+(b2-a2)+...+(bn-an)<=(a2-a1)+(a3-a2)+...+(f(b)-an)

finish the proof from here.