- Empecé la carrera de Historia del Arte pero la dejé --> I started the History of Art degree but I quit it or I started the History of Art degree but I dropped out of it (are both correct?)

- Iba a hacer la carrera de Economía pero al final cambié de opinión y decidí hacer la carrera de Ciencias Políticas --> I was going to do the Economics degree but in the end I changed my mind and decided to do the Political Science degree

查看翻譯

Above it correct and makes sense but as a native speaker I’d say

I started the History of Art degree but I quit it ( could say quit without the it) or I started the History of Art degree but I dropped out of it ( again it makes sense but I’d say dropped out ( without the” of it “bit) - not sure why but sounds more natural but your version makes more sense - I think “ to drop out” is a phrase that implies dropping out of something so no it needed

Below is totally correct
- Iba a hacer la carrera de Economía pero al final cambié de opinión y decidí hacer la carrera de Ciencias Políticas --> I was going to do the Economics degree but in the end I changed my mind and decided to do the Political Science degree