Summing Cells In Column Based On Data In Another Column?

I have a statement from an account (which happens to be the government) in which they list every invoice they are paying and each item on that invoice. But they don't have an invoice total. I'd like a way to add up the item totals for each invoice and put the total in column D. Each invoice could have 1 to 10 different items on it.

A(invoice#) B(Item) C(total) D(invoice total)
111 widget 1 $5
111 widget 2 $10
111 widget 3 $8 XXXXX
222 widget 1 $5
222 widget 5 $15 XXXXX
333 widget 2 $10 XXXXX
444 widget 5 $15 XXXXX

I had thought an IF formula would be the way to go.