A particle moves from $(1,0,1)$ to $(0,0,1)$ along a straight line, and then to $(0,1,1)$ along a straight

line, and then back to $(1,0,1)$ along a quarter circle of radius $1$ in the plane z $=1$ centered at

$(0,0,1).$ If the particle experiences a force from a field F$($x$,$ y$,$ z$)=$z$2$ y$,2$x $$ ez $,3+$ z$,$ how

much work was done by the field on the particle as it traversed the path? $($In other words, what is

the integral of F along the path described in the first sentence?$)$