You can divide by the class width before you integrate instead of afterwards, but that's pretty much the same thing. Other than that, I don't think there's a way.

Yes. So, in your example, that would be ∫ (x/10)dx. As I said, they're really just the same thing in a different order.

You are getting a little confused with the notation. f(x)=x^2 is the same thing as y=x^2.  f'(x) is the same as dy/dx=2x.  Taking an integral is the exact opposite of taking an integral.  An integral is also called an antiderivative.  ∫dy = ∫2x dx is the same as y=x^2. 

  Too many people get hung up on the different notation.  In my opinion, you should become more comfortable with the dy/dx type than the f'(x) kind.  It makes the higher maths a little easier to grasp. 

  Those increments are the most important piece of calculus to understand.  Without those increments you really can't understand limits.  And limits are used as the basis for almost all of calculus' proofs.

   By the way if you want to remember to divide by the "class width" in a general way, just divide your function by (b-a).  They are constants and will not affect your integral.  But that is more general notation.  a being the upper and b the lower bound of a definite integral.

Yes, but it will still have the last edited by... bit so people will know that something's up. Plus, my post is here now.