Only the wiki it says something different
If cup winners had
already qualified for European competition through
league performance, their place through the
league is vacated and goes to the best ranked teams not
qualified for European competition. This means that the
cup runner-up is no longer
qualified through the
cup berth
Plus this was last year.
Manchester City, Chelsea, Wolves and Manchester United all play in Europe next month. If any of them win their trophy, they will go into next season's Champions League group stage no matter where they finish in the league.
If Manchester City (who lead Real Madrid 2-1 in the last 16) win the Champions League, it makes no difference to the European places in the Premier League - England would not get any extra places.
But if Chelsea (who trail Bayern Munich 3-0) win the tournament and finish outside the top four, then five English teams would go into next year's Champions League with two in the Europa League.
Maybe I am reading the question wrong, I am in and out of class.
Who needs what to qualify for Europe?