`a(t)=t^2-4t+6`

`a(t)=v'(t)`

`v(t)=inta(t)dt`

`v(t)=int(t^2-4t+6)dt`

`v(t)=t^3/3-4(t^2/2)+6t+c_1`

`v(t)=t^3/3-2t^2+6t+c_1`

`s(t)=intv(t)dt`

`s(t)=int(t^3/3)-2t^2+6t+c_1)dt`

`s(t)=(1/3)(t^4/4)-2t^3/3+6t^2/2+c_1t+c_2`

`s(t)=t^4/12-(2t^3)/3+3t^2+c_1t+c_2`

Let's find constants c_1 and c_2 . given s(0)=0 and s(1)=20

`s(0)=0=c_2`

`s(1)=20=1/12-2/3+3+c_1`

`20=(1-8+36)/12+c_1`

`20=29/12+c_1`

`c_1=20-29/12=211/12`

`s(t)=t^4/12-2t^3/3+3t^2+211/12t`

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