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You got question 1 wrong. According to your answer the work for a spring would be linear, for which it's not. The force for a spring is linear, not the work. And why would you integrate from 1 to 6 and not 0 to 6, and 1 to 12 and not 0 to 12? The spring force goes according to F(x) = - k * x, where x is the distant the spring is moved from it's natural length. See if this helps you at all.
I haven't tried your second question yet as it sounds a bit confusing to me.
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