integral limits from 0 to 1 x^2(1+x)^2dx=

0 to 1 integral x^2(1+x)^2dx

=0 to 1 integral x^2(1+x^2+2x)dx

=0to 1 integral (x^2+x^4+2x^3)dx

=0 to 1 integral x^2dx + 0 to 1 integral x^4dx + 2* 0 to 1 integral x^3dx

=0 to 1 [x^3/3] + 0 to 1 [x^5/5] + 2* 0 to 1 [x^4/4]

=[1/3-0/3] + [1/5-0/5] + 2*[1/4-0/4]

=1/3 + 1/5 + 2*1/4

=1/3 + 1/5 + 1/2= 31/30

are yar

u just expand  (x+1)²

and multiply by x²

u will get x²  +x⁴  +2x³

now on integrating u will get x³/3 + x⁵/5 + x⁴/2 and on putting limits

u will get 1/3+1/5+1/2=31/30

 good luck

i think the ans is 31/30....."is it right??"

Yes 31/30 is right.