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