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getting Limit[] to evaluate


I wanted to compute the following definite integral, where b > 0

	In[1]:= Integrate[x (1-x)^b,{x,0,1}]

	Limit::nlm: Could not find definite limit.

	                                       1 + b           2 + b
	          1       1             (1 - x)         (1 - x)
	Out[1]= ----- - ----- + Limit[-(------------) + ------------, x -> 1]
	        1 + b   2 + b              1 + b           2 + b


The problem is that it doesn't know that b is not -1 or -2.  In this
particular case, I can see "by inspection" that the Limit[...] term
evaluates to zero, but how can I get Mathematica to do this itself?

  -- David Jacobson



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