integrate(x^(3-1)*(1-x)*(3-1),x,0,1)

Why is this returning 1/6 and not 1/30?

More generally why is 

integrate(x^(ai-1)*(1-x)*(bi-1),x,0,1)

returning (bi - 1)/(ai^2 + ai) and not beta(ai,bi) as it should?

Running this on SMC.

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