Summing a variable number of cells

Hey all,

Have a look at the row below: (Sorry I cant attach files for some reason)

A B C D E F G H I
12 13 45 22 45 46 70 5


I'm looking for a formula for column 'I' that would add the numbers on the row according the the number in cell H1.

so in this example, because 'H1' =5 , cell 'I1' would be sum(A1:E1)

and if 'H1' was 4, then cell 'I1' would be sum(A1:D1)


Any help is really appreciated

Thanks
Lovi