EDITThe interval was unspecified. Please check the interval on which the density is defined and put it in place of [a,b]
to speed up your integration.
clearly the region isn't all of so that integration is incorrect
NEXT comment, the region is most likely (0,1) and that means this is a Beta(1,3)
you can look up it's variance in that case.
Yeah, it was unspecified so I just kinda went to default. Thanks for catching that.