Yes, it is safe to do an upper and lower body workout in the same day. Total body workouts are great for burning calories and are great for those who have limited time. However, you want to give your muscles a day in between (48 hours or more depending on the intensity–more intense may need a few days) before working the same ones again.
It may, however, depend on one’s goals, intensity, and fitness level. Some people prefer to split up their lifting workouts. Upper body, lower body, core, push/pull muscles–these are all examples of different workouts, just as working chest/tris/bis. Again, it just depends on one’s goals and the amount of time they have to hit the gym.
Hope this helps!
It is certainly safe to train all muscle groups on the same day. I personally recommend working each muscle group at least twice but no more than 3 days per week, with at least one rest day in between working any specific muscle group. Thus if you complete a full body routine every workout day, you wouldn’t want to weight train more than 3 days total per week with a rest day in between each workout.
If however, you want to train with weights more often then 3 days per week you could complete a split routine (such as lower body one day, upper body the next; or dividing it further into muscle groups, etc).
Personally I like completing 1 upper body, 1 lower body, and 1-2 full body routines each week; the second full body routine an easy day for trying new exercises or having a light workout day. An example schedule would be:
Monday – Upper Body
Tuesday – Lower Body
Thursday – Full Body (heavy day)
Saturday – Full Body (light day)
This is only one example; you would want to experiment with what works best with your schedule and your body. There are an infinite number of ways to divide your workouts; here’s a blog I wrote with many examples: http://www.integratedfit.org/webblog/?p=36. Rest between the workouts is just as important as the workouts themselves; so remember that it’s not just about the days you train, but the days you train well.
I train upper and lower together every workout. I split my workouts up either push day or pull day on a 3 day/week cycle. Push day quad based exercises (even deadlifts), chest, triceps, and overhead pressing for shoulders. Pull is hamstrings, lats, biceps, rear and lateral delts. I do calves on either of the days. This gives me a push/pull/push one week, pull/push/pull the next. Every now and then, I do one of each plus a full body for my 3rd. You could do 2 push and 2 pull a week as well with that split.