There is a discussion https://sourceforge.net/p/maxima/mailman/maxima-discuss/thread/1130339961.5365646.1494311181007%40mail.yahoo.com/#msg35829809
about a wrong result of integrate(f,y,0,1). It was suggested to report a bug.
It seems that the function f defined in (i2) makes the maxima-function integrate() to fail.
(i1) bug_report();
(%o1) ... build_info(version="5.38.1",timestamp="2016-10-19 00:27:24",host="x86_64-suse-linux-gnu",lisp_name="CLISP",lisp_version= "2.49 (2010-07-07) (built on cloud112 [127.0.0.1])") ...
(i2) f:(y^2-1)*asin((sqrt(1-y^2)*sqrt(y-y^2))/(y^2-1))$
(i3) integrate(f,y,0,1);/* wrong answer */;
(%o3) -(15%pi+32)/45
(i4) integrate(expand(f),y,0,1);/* right answer */;
(%o4) (15*%pi-32)/45
Diff: