The domain of f(x,y) is the xy-plane, and values of f are given in the table below.
0 1 2 3 4
0 60 60 60 62 64
1 61 61 62 61 60
2 65 68 68 68 70
3 63 61 60 60 62
4 59 55 51 48 45

Find [tex]\int\limits_c grad f . dr[/tex] , where is
(a) A line from (0,1) to (1,2).

(b) A circle of radius 1 centered at (1,2) traversed counterclockwise.