I integrated the function between x=5 and x=9 and got 60 joules. Then I set that equal to (1/2)mv^2 and solved for velocity. I got 9.60 m/s. Is this correct? My professor said the answer would be about 9 m/s.

I get an answer much closer to 9 m/s (not exactly 9 though). Show us your work - the integral of Fdx from x = 5 to x = 9 is not 60 joules (be careful of the sign of the cubic portion of the integral).