Categorical vs continuous feature selection/engineering
For encoding categorical features, there is two common ways:


  Ordinal encoder


This is the way you mentioned as 'encoded as integers'. In this method, an integer starting from 0 is assigned to each category. The problem of this method is that it randomly prioritize categories. So in cases when there is no priority among categories, this encoding is meaningless as you mentioned. The only case it work is when assigning larger integer to some categories is meaningful.


  One-hot encoder


This method makes a feature vector (one-hot vector) for each categorical feature which is the same size as the number of categories. The method assigns each component of the vector to one of the categories. For each data sample, it assigns 1 to component which its corresponding category is present at the sample and assigns 0 to other components. The benefit of this method is that unlike ordinal encoder it does not prioritize any category.

So in your case, I highly recommend that you use one-hot encoder.