Before revision:  A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's  .
After revision:  A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's . Finally, we show the existence of \int_0^t\phi d\omega for a c\`adl\`ag \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .