When you integrate what do you need to add on the end ?

When integrating you must always add a constant on the end. If you think about it backwards, it is because adding a constant when differentiating an expression doesn’t change the output, therefore there are multiple expressions all with different constants whose derivative is the expression you are integrating, thus you should add a constant at the end of your answer so that you have included all possible solutions via a general solution with a constant.