In RISK, when it is your turn and you have all the countries for a continent, do you have to place the bonus armies on the continent or can they go anywhere you have armies on the board?
Looking at the rules here They say with emphasis mine:-
Territories. At the beginning of every turn (including your first), count the number of territories you currently occupy, then divide the total by three (ignore any fraction). The answer is the number of armies you receive. Place the new armies on any territory you already occupy. Example: 11 territories = 3 armies 14 territories = 4 armies 17 territories = 5 armies You will always receive at least 3 armies on a turn, even if you occupy fewer than 9 territories.
Continents. In addition, at the beginning of your turn you will receive armies for each continent you control. (To control a continent, you must occupy all its territories at the start of your turn.) To find the exact number of armies you’ll receive for each continent, look at the chart in the lower left-hand corner of the game board.
To clarify, you relieve armies on any territory you control. There is nothing in the rules for continent bonuses that say ,just go on the continent. it just says "you receive them" and the rule above that is to place any territory you control.
I think you are confusing this with another rule. That is, when you turn in three cards to get armies, you will get "bonus" armies if you own the territori(es) represented by one or more cards. Those bonus armies have to go on the respective territories (but not the "main" armies you received for the three cards).
The armies you get for owning a continent each turn continue as long as you completely own that continent. They represent "income," and are not specific to that continent. In this regard, they are like the income you received by dividing the number of territories you have by three. This is also "not specific" to the continents that your territories lie on.