Bug in limit or integrate

On Jan. 1, 2012, Barton Willis wrote:
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>Some definite integrals of exp(-x^4) are broken:
>
>  (%i6) integrate(exp(-t^4),t,0,1);
>  (%o6) (%i*(gamma(1/4)-gamma_incomplete(1/4,1)))/4
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the definite integral of the real function exp(-x^n)  over
the real interval (0,1) is broken (spurious imaginary parts,
wrong real parts) for n = 3 through 15, and probably forever.
-----------------------------------------------------------------
(%i1) exp_test(n) :=
  ( print (n,"  qags = ",  first( quad_qags (exp(-x^n),x,0,1)),
           "   integrate = ",
          expand(float(rectform(integrate(exp(-x^n),x,0,1))))))$

(%i2) for m thru 15 do exp_test(m)$

1   qags =  0.63212055882856    integrate =  0.63212055882856
2   qags =  0.74682413281243    integrate =  0.74682413281243
3   qags =  0.80751118213967    integrate = 
0.69932519757296*%i-0.40375559106984
4   qags =  0.8448385947571    integrate =  0.8448385947571*%i
5   qags =  0.87007466768589    integrate = 
0.82749018236601*%i+0.26886785869008
6   qags =  0.88826369875194    integrate = 
0.76925892837871*%i+0.44413184937597
7   qags =  0.90199160301324    integrate = 
0.70520543215755*%i+0.56238256584096
8   qags =  0.91271857185875    integrate = 
0.64538949147622*%i+0.64538949147622
9   qags =  0.9213308364909    integrate = 
0.59222004611848*%i+0.70578036756801
10   qags =  0.92839720283799    integrate = 
0.54569818409775*%i+0.7510891146261
11   qags =  0.93429939205577    integrate = 
0.5051203870693*%i+0.78598266428894
12   qags =  0.93930307080183    integrate = 
0.46965153540091*%i+0.81346032116712
13   qags =  0.94359882032526    integrate = 
0.43851223691831*%i+0.83551526125626
14   qags =  0.94732690220079    integrate = 
0.41102973849353*%i+0.85351204660935
15   qags =  0.95059283193    integrate = 
0.38664093739113*%i+0.86840976367727
------------------------------------------------
Ted