I'd rather use Green's Theorem.
BUT if you wish to do this directly you need to figure out the three lines parametrically.
From (0,0) to (1,0)
you can let y=0, x=t where 0<t<1
note that dy=0, dx=dt
From (1,0) to (1,3)
you can let y=t, x=1 where 0<t<3
here dy=dt, dx=0
Finally you have
(1,3) to (0,0)
you can let y=3t, x=t BUT 1<t<0 since you are heading to (0,0)
then dy=3dt, dx=dt