another question on line integral

i have to evaluate the line integral

∫c (xy)^2 dx + xy^2 dy

where c is closed curve formed by x=1 and y^2=x

for this question. i drew a diagram which has three sides.

c1 : x=1, y=t, 0<t<1

c2 : x=t, y=0, 0<t<1

c3 : x=t , y=x^1/2 , 0<t<1

the book says the answer is 4/15. but i keep getting wrong answers

where did i make mistake??