Find the work done by the force F(x) newtons along the x-axis from x=a meters to x=b meters.

F(x)= $\displaystyle x \sin (\frac{\pi * x}{4})$

I understand we need to use an integral from a to b.

What I don't understand is how to change the intervals when doing anti differentiation by parts, or if they even need to be changed at all.

Also, why do we need the integral? It seems like this is a simple F(b)-F(a) problem.

Thanks!