applying formulas using cell references

Hi - I'm new here. I've looked over a few pages of posts but didn't find a topic I thought would address what I would like to do.

Suppose I have the numbers 1-10 in cells A1-A10 respectively

suppose in cell A12 I have a value x and in cell A13 I have a value y.

I would like to put a formula in cell A15 that sums up the values in cells Ax to Ay. For example, if the value in cell A12 is 4 and the value in cell A13 is 6, the result of the formula in cell A15 would be the sum of A4,A5,A6 = 15.

I have had no luck coming up with a formula that does this, or in searching for a formula that does this. A little help, please?

Thanks,
Peter