There are more stillbirths in the 43rd week (i.e 42+anything) than in the 41st and the difference is therefore factored to be in the 42nd week, so they induce you in the middle of it in some places, treating it as a window of opportunity for preventative medicine. It is NOT an evidence based practice, induction at 41+10 has not been proven to reduce stillbirth rates (i.e. the level remains the same for babies born in the 41st week whether by induction or not, and there is no way to determine how many of those babies who are induced would have been born before 42 weeks anyway) and HAS been shown to increase the c-section rate and risk of injury to both mother and babe.
And FWIW unless your ob offers foley's catheter inductions i would be surprised if they offer to induce you at all. Cytotec, prostin and pitocin have all been shown to dramatically increase the uterine rupture rate in VBAC labours.
Bx