The area bounded by the curve y=x^4-2x^3+x^2+3 , the axis of

abscissas and two ordinates correponding to the points of minium of the function y(x) is

f(x) = x⁴ -2x³ +x² +3

f_{¹(x) =} 4x³ -6x² +2x

on putting f¹(x)=0

 x=0,1/2 ,1

now f²(x) =d²y/dx² =12x² -12x +2

f²(x) is +ve for x=0,1

hence its minimum is at x=0,1

now area bw curve and x=0,1 is

area =A= f(x)dx     limit 0 to 1

              =x⁵ /5 - x⁴ /2 + x³ /3 +3x       lim 0 to 1

               =91/30 square units