I suggest using supervised learning and employing a linear model: linear regression.
This is a perfectly linear system (y=x+1), so linear regression will work just fine i.e. perfectly. Further, you have an infinite amount of data you can use to train the system, so it should be easy to train ;-) I jest... I think that two data points will be sufficient, again, since it is perfectly linear!
Pedagogically, the triviality of this extremely simple linear system gets a little more interesting when you try analogue based methods like support vector machine (SVM) - which should also be able to provide a perfect result, decision trees or random forests, and even naive Bayes regressors.
Though its useful to start learning with very simple systems, I suggest quickly moving on to something more complex, i.e. don't get too stuck in your own head for the trivial linear model. Don't forget that the power of data science and machine learning lies in its statistical nature, so try to find a test case that includes some statistical variation in the input.
Hope this helps!