This is an interventional study where hospitals in Belarus were randomised to a breastfeeding promotion programme or not. There was a moderate effect of this programme on bf vs ff rates (especially at 1 year) and a very striking difference in ebf vs mix feeding rates.
The children in the intervention group had higher IQs at 6.5years of follow up.
news.yahoo.com/s/nm/20080505/hl_nm/breastfeeding_dc_4 www.eurekalert.org/pub_r eleases/2008-05/jaaj-bmi050108.php
Arch Gen Psychiatry. 2008;65(5):578-584.
No research study is perfect, and you can't say just from this that "long term exclusive BF boosts IQ", nevertheless the evidence for a real effect is fairly good.
And my personal take on it is that I'd be wanting it not to show an effect since I am mix feeding... meh.