Beware the DST issue! The "addDays" function is not DST-aware, so if you step over a DST transition during the addition of days (in a time zone that has DST) then the time will be messed up.
To resolve this one split the date/time into separate date and time parts first, add the days to the date part then re-combine at the end, like:
DateTime dt = ...;
Integer days = ...;
Date d = dt.date().addDays(days);
Time t = dt.time();
dt = DateTime.newInstance(d, t);
If you are working in the UK (London) time zone the following anonymous Apex illustrates the issue nicely:
DateTime dt = DateTime.newInstance(2017, 10, 28, 23, 59, 59);
System.debug('Adding days directly: ' + dt.addDays(2));
Date d = dt.date().addDays(2);
Time t = dt.time();
dt = DateTime.newInstance(d, t);
System.debug('Adding days in parts: ' + dt);
Hope this helps!
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