You can't find how far the car travelled mathematically. You can't get it by integrating anything because you have no function to integrate. The acceleration isn't constant in one gear never mind two gears.
Two solutions, log instantaneous acceleration vs time. (gtech does this but only to output time and speed, it could output distance but doesn't)
Measure the damn distance covered to get to 60.
Erice1984, you used a gtech to get your numbers, go back and do them again. Then measure the distance travelled. That's really the only simple way to get the answer you want.