As Mr. William already guided you on to right way, just few lights on the functioning.
INTEGER-OF-DATE function returns value as an integer that is the number of days that the input date succeeds December 31, 1600 in the Gregorian calendar. The function result is a seven-digit integer with a range from 1 to 3,067,671.
So basically INTEGER-OF-DATE(INPUTDATE) would return an integer representing number of days between 12/31/1600 and your input date.
So now you should not be having problem understanding how this works:-
COMPUTE NUMBER-DAYS-1 = FUNCTION INTEGER-OF-DATE(YYYYMMDD). //*input date 1
COMPUTE NUMBER-DAYS-2 = FUNCTION INTEGER-OF-DATE(YYYYMMDD). //*input date 2
COMPUTE DIFFERENCE-DAY= NUMBER-DAYS-1 - NUMBER-DAYS-2.