Well, it's just using the area of the trapezium...
breaking the curve down to trapeziums, finding the individual areas and adding them up
0<x<0.2
a= 1/2 X(sum of parallel sides) Xheight
= 1/2 X(1+ 1.246) X 0.2
repeat this for each
0.2<x<0.4, 0.4<x<0.6, 0.6<x<0.8,0.8<x<1
adding up the area for each gives u ans as 1.8278
