Hey guys ! I just need a little help on a integral I was trying to solve using feyman's technique.

This is the integral from 0 to 1 of (sin(ln(x))/ln(x) dx, which has been solved in one of the videos of bprp, but I'm trying to solve it using a different technique, and I end up with a different result, which is false of course, but the thing is I wanna know where I messed up (not sure, but I have a feeling it's on point 5 where I calculate the constant)

Those are my steps :

-step 1 : I do a u sub and define my function I(alpha)

-step 2 : I do the partial derivative with respect to alpha of I(alpha)

-step 3 : I find the antiderivative of sin(u)exp(alpha*u)

-step 4 : I plug my antiderivative into my integral, and calculate it. Then I integrate back I'(alpha) to find back I(alpha)

-step 5 : I use the limit as alpha goes to -inf to make the integral equals to 0 to be able to calculate the constant

-step 6 : I use I(1) to calculate the integral, but in the end I find -3pi/4 instead of pi/4.

Do you guys know where I messed up ? That would help me a lot, thanks !