how retrieve itunes ipad apps after OS failure to new os

[lse123]

Only free app I have, well if I did not sychr yet ipad to new computer and have just installed itunes and, old computer os failed, can not run itunes, only backup etc files can get, may transfer all old backup folder to the new computer(itunes/backup)? this will bring all old apps back to itunes? what to do to bring all old apps back to itunes by this? where paste, what data from old to new itunes?

coping backup folder to new os backup folder will appear in itunes the (only free I had) apps? is needed after that any action to retrieve them from backup or?