integrate of bessel_i sign error?

On Oct. 22, Dieter Kaiser wrote:
>Yes, I think the integral of bessel_i(0,x) is wrong:
>
>(%i1) integrate(bessel_i(1,x),x);
>(%o1) - (bessel_i(0, x))
>
>The correct answer should be bessel_i(0,x), see e. g.
>http://functions.wolfram.com/Bessel-TypeFunctions/BesselI/21/01/01/
>
>I will correct it.

I checked with Wolfram Alpha:

A review of the integrate of bessel_i bug:

(%i4) f(bessel_i(1,%i*1.5));
(%o4) 0.5579365079101*%i
(%i5) f(integrate(bessel_i(1,%i*y),y,1,2));
(%o5) -0.54130690741673*%i

integrate appears to produce the wrong sign
for this integral??

Here is Wolfram Alpha answer:
NIntegrate[BesselI[1,I*y],{y,1,2}]

 ----> %i*(bessel_j(0,1) - bessel_j(0,2))

  ------->  0.541307 

Check   using maxima:
  (%i2) f(%i*(bessel_j(0,1) - bessel_j(0,2)));
(%o2) 0.54130690741673*%i

Ted