Question 876816
{{{graph(300,300,-3,3,-3,3,x*(x-1)^2)}}}
From the graph, it looks like the limits of integration are {{{x=0}}} and {{{x=1}}}

{{{int((x*(x-1)^2),dx,0,1)=int((x^3-2x^2+x),dx,0,1)}}}
{{{int((x*(x-1)^2),dx,0,1)=x^4/4-(2/3)x^3+x^2/2+C}}}

{{{int((x*(x-1)^2),dx,0,1)=1/4-2/3+1/2}}}

{{{int((x*(x-1)^2),dx,0,1)=1/12}}}