Solve using Work formulas using calculus if needed.?

Question

A 150 g bullet is fired from a rifle with a barrel of length of 65 cm. The bullet starts from rest at one end of the barrel and experiences a position-dependent force due to the expanding gas given by F(x) 15,000 + 10,000x - 25,000xsquared in Newtons with x in meters.
1. Calculate the work done on the bullet by this force over the length of the barrel.
2. Assuming that this is the only force doing work on the bullet (neglect friction) find the speed of the bullet as it leaves the rifle.
Please show all work so i can understand how to do the problem

Answer 1

W = Int (0,0.65) F(x) dx = -25,000/3(0.65)^3+10,000/2(0.65)^2+15,000(0.65) Nm=9750Nm
360
F= m* dv/dt = m*dv/dx*dx/dt but dx/dt =v
F = m*v*dv/dx and
F*dx=m*V*dv
so W =1/2mV^2 and V = sqrt(2W/m) = 360.56m/s
In other words all the work done is transformed into kinetic energy