How to carry units in integration

[Liketothink]

Homework Statement

I am trying to integrate from 0 to 10 ft -4x^2/2+4x. I am solving for deflection. The forces are in kips. Somehow the book ends up with k-ft^3. I don't understand how I would carry units in an integration. Any help please?

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

Normally integrating gives an area which would give the product of the units on the axes. I'd be inclined to think you'd get kip-ft. Are you sure the units are correct?