Before revision:  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 .
After revision:  Finally, we propose a tentative definition and 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 .