Does student integration in schools matter in order to ensure educational equity?

In my opinion,  student integration is not a huge factor in order to ensure educational equity. Although it is important to integrate schools, it is not the most important issue when dealing with educational equity. What I think matters in ensuring equity in schools is proper funding and location. Personally, I go to a private boarding school in Rhode Island whose population (students and teachers) is predominantly caucasian. However, it's a great school not because it has a huge concentration of one single race, but rather because of its ample funding. As a result, it is needless to say that people with more money will have a better education than those who have less. Is this fair? Not necessarily. But that is just how the world works.