Botany

It is really difficult to say that Integrated MSc with Phd is available or not. Because there are a lot of private universities who are offering these courses in integrated manner. that is Masters degree along with Phd Degree at a stretch of 5 years (2+3) but it will be difficult to say that if that courses are accredited by national boards. because normally the boards accept regular courses.
They consider integrated courses as distance courses and hence have no equivalency with regular ones. hence it would be wiser if you pursue you MSc and then apply for Phd and complete Phd after completion of masters only. again you have asked for completing the integrated course in distance mode. sorry to say that already you are losing charm of the degree by choosing integrated one on top of that distance course mode will make it horrible.And even i don't think it will be available as integrated course in distance mode.
That means the universities might not be offering integrated courses in distance mode. you have to check out from the respective universities only.One of the universities which may offer this integrated degree is Centurion University.