解:A∩B={-3},
∴-3∈B.
∵a2+1＞0,
∴集合B中等于-3的元素只有a-3或2a-1两种情形.
(1)当a-3=-3,即a=0时,A={0,1,-3},B={-3,-1,1}.这时A∩B={-3,1},与已知A∩B={-3}矛盾,故舍去a=0;
(2)当2a-1=-3,即a=-1时,A={1,0,-3},B={-4,-3,2},符合要求.
因此A∪B={-4,-3,0,1,2}.
