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Default Using Sum function dynamically

I am trying to figure out how to adjust the range of cells which are summed based on the value within another cell.

so if I had =sum(a1:f1) but I wanted to have the start and end points be dynamic from a column perspective (the row would remain constant). So based on the value of cell a10 and b10, for instance, the starting and ending column position might change to be B1 and E1 or some subset or expansion of A1:F1.

From some of what I have found I think I use INDIRECT but the examples don't reflect what I am trying to do exactly.

Thanks for any help

David
 
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