The area bounded by y=1x2−2x+2 and x -axis.

y=1(x−1)2+1 When x=1,ymax=1  When x→±∞,y→0  Therefore, x -axis is the asymptote.   Also f(1+x)=f(1−x) Hence, the graph is symmetrical about line x=1  From these information the graph of function is as shown in  adjacent figure.  Area =2∫1∞ 1(x−1)2+1dx=2tan−1⁡(x−1)1∞=π sq. units