Question: Strange equation to solve

Hello people, I have a question about an equation, I have to solve on maple.

 

So i have

>p:=a+bx+cx^2+dx^3;

>I1:=int(p(x),x=0..1);

>I2:=int(x*p(x),x=0..1);

>I3:int(x^2*p(x),x=0..1);

>I4:int(x^3p(x),x=0..1);

and i have to find a,b,c and d

the only thing i know is that I1=1, I2=0, I3=0,I4=0

 

can someone can help me. Thank you

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