1. ## proof

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.

2. Can you give an example of just you are doing?
Suppose for example,
$\tan x$ its jump points can be enumerated. Now what?