Conditional Sum: Simple but very frustrating question

Hello All,
I have a quite simple need but I cannot find the right syntaxe

start end A X Y
10 30 15 46
40 90 2 48
60 80 3 50
80 110 0 52
70 130 26 54
90 100 5 56
20 70 0 58
40 60 1 60
60 90 0 62
20 90 3 64
50 70 2 66
68
70
72
74

I have to calculate Y for each X value. Each Y should be the sum of the whole column A, with some condition. The condition is that the A value will be summed if the X value corresponding to the Y we calculate, is >= to the start and <= to the end.
What is the exact function syntaxe I have to use in the Y column ?

I would be so thankfull if somebody could help on that.

Filipp