work done by lifting block attached to spring

this problem is in my calc book.

If one hangs a spring (of constant 10lbs/ft) vertically and attaches a 10lb. weight to the spring, how much work is done in raising the weight 6 inches from where it hangs naturally?

i drew a free body diagram and deduced that when you are lifting the weight up, the forces of gravity and spring force act downward (since spring force always acts opposite to displacement). so my equation for force is F = mg + kx = 10 + 10x. so i took the integral of that from 0 to 1/2 and i got 6.25 ft lbs or 75 in lbs. but my book's answer is 240 in lbs. how did they get that?