y'=√sinxy'^2=sinxs=∫（a,b）√1+sinxdx=∫（a,b）√（sinx/2+cosx/2）^2dx=∫（a,b）（sinx/2+cosx/2）dx (此处都取正值）=2∫（a,b）（sinx/2+cosx/2）d（x/2）=2sinx/2-2cosx/2|(a,b)=2sina/2-2sinb/2-2cosa/2+2cosb/2.
