According to the meaning of the question, f(x) is odd function, and we only need to discuss the case that x belongs to [0, positive infinity].

When x belongs to [0, 1], f (x) = x;

f( 1)= 0；

When x belongs to (1, positive infinity), f (x) =-x.

The left limit of f(x) at 1 is 1, and the right limit is-1, and the function value at 1 is discontinuous, so the function at-1 is also continuous.

So the discontinuity of f(x) is plus or minus 1, which is the jumping discontinuity.