Here's an overview of the process. Post again if you're still having trouble.
Take a horizontal slice through the trough. Let x be the distance from the top of the trough.
The width of this slice is calculated by fitting a line to the two points w=3m when x=0, w=1.5m when x=3m.
The volume of this slice is length times width times height: dV=(10m)(w)(dx)
The weight of this slice is density times volume times g: dF=(1000)(dV)(9.8)
The work done to pump this slice out of the trough is weight times distance: dW=(dF)(x)
And then you add up the work for all the slices:
Once you substitute everything, you should have the integral of some function of x (the dx is buried in all the substitutions), and in this case it is pretty easy to solve.
If you like to keep track of units (I always do), remember the conversions and .