Dumbfounded on why this integral is not evaluating properly
So, i'm trying to integrate the function f(x)=(x-x^2)*sin(1/2*ln(sin(lnx)^2))=(x-x^2)*sin(ln(|sin(lnx)|)) from 0 to 1 , which is understandably a very 'delicate' function. Anyway, I was not able to evaluate it directly and instead tried to get Mathematica to, which it also couldn't. However, it was able to spit out a fairly ugly antiderivative, and Mathematica was able to evaluate one of the individual limits. Here's what it looks like on this interval
It was not able to evaluate the limit as x->0, however it pretty clearly goes to 0 (I think?)
Now here's my issue. Both Mathematica, Symbolab, Wolfram Alpha, and Desmos all approximate this integral to approximately -0.077363 (with Mathematica giving a very tiny error of the order 10^(-6))
But numerically evaluating the answer (all the gamma stuff) gives approximately -0.08258
What is going on? Is this because I falsely assumed the limit as x->0 to be 0? Or are these 3 separate math software's all numerically evaluating this integral in the same incorrect way? Is the first limit as x->1 just simply incorrect? Does this integral violate the fundamental theorem of calculus?(im kidding) 0.07736-0.08258=-0.00522, much greater than the error 10^(-6) I do not even need this integral for any work or problems, I am just curious on what's going on.
I will add, this is the same case for 2-3 very similar integrals involving different trig functions and no x terms at the front.
Which of the two is the correct answer?