[math-fun] An Unusual Integral?

3==Integrate[Hypergeometric2F1[1/3,2/3,1,x-(1/4)*x^2],{x,0,2}] ( Cf. https://oeis.org/A006480 and thereafter ) Gosper said that this calculation was "weird". I think it would be rare to get an integer value from an integral of 2F1(a,b,c,z), with non-cancelling (a,b,c), z=P(x) in Q[[x]], and z over 0...1, between D.E. singular points. Does anyone else have an opinion? --Brad