The new account will get the activity of the old one in addition.
That is the old posts will be associated to the new account so that you have access to your old posts (e.g., for editing); and, you will also get the associated points (the points of the old account) in addition to the ones you have on this account. So, yes, the points simply add (in most cases or almost, see below).
Basically, it should be as if you always had had just one account.
(Side remark: strictly speaking, it should not always be true that the points of the merged account is the sum of the points before the merge, due to things like capping of gained points from votes at 200 per day, but by and large and especially for smaller accounts it should be the case.)