Importance of feature selection for boosting methods
There is a difference between boosting and features selection. 
It is very important to understand that the original boosting algorithm or bagging algorithm have been modified and augmented with many features selection and/or data sampling ( over/ down/ synthetic) to improve the accuracy. 
Let us talk about the difference between bagging and boosting : 
Booth of them are random subspace based algorithms, the difference is in bagging we used uniform distribution and all the samples have the same weight , in boosting we use non- uniform distribution, during the training the distribution will be modified and difficult samples will have higher probability. The second difference is the voting. In bagging it is average voting , in boosting it is an weighted voting.

Features selection algorithms try to find the best set of features that can separate the classes. But there is no explicit consideration for difficult or easy samples and what is the used training algorithm. 
In boosting, the algorithm selects the feature that minimize the error , the error is the sum of prob "weights" of samples that miss classified, since the difficult samples have higher weights , the selected feature will be the one that better distinguish between the difficult samples. 

FE ( Features, data) --> feature set
Boosting ( features, data, base learners type, initial distribution, difficult samples) --> feature set