Physics- Given Force find change in kinetic energy?

Question

A force (F) acting on a body depends on the position of the body (x) as F(x) = -3(x) + 2x^2

Assuming this is the only force acting on the body, what is the change in kinetic energy of the body as it moves from x=1 to x=2?

ANSWER : 166 2/3 mJ

How do I do the work for this problem? Change in kinetic energy is = 1/2mv^2 - 1/2mvo^2 but I m only given Force? No mass or velocity so I m confused.
I have only found that
F(1) = -1N and F(2)= 2N.

Some Body · Accepted Answer

Force times distance is work.  The change in energy is equal to the work done.
W = ∫ F dx
W = ∫₁² (-3x + 2x²) dx
W = (-3/2 x² + 2/3 x³) |₁²
W = [(-3/2 (4) + 2/3 (8))] - [(-3/2 + 2/3)]
W = -6 + 16/3 + 3/2 - 2/3
W = -36/6 + 32/6 + 9/6 - 4/6
W = 1/6 J

Or, W = 166 2/3 mJ.

Physics- Given Force find change in kinetic energy?

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