text: Choose indefinite or definite integral
  
  I have an equation like this
  
  $dW=x\,dx$ , where W is work.
  
  I have find a lot on internet, but I wasn't able to find clear information. I have two questions:
  
  1) If I want to integrate this equation, do im forced to apply definite integral or indefinite integral at the same time to each member of the equation ?
  
  2)The right part of the integral is quite clear to me, for example I can integrate between $x=0$ and $x=5$. But in the left part, what's the meaning to integrate between (for example) $W=4$ and $W=8$ ?
  
  If you are finding the work between two points you can integrate the right hand side from between any values of $x$.
  and the left hand side between any values of $x$ as W is a function of$x$.
  That being said , if you are integrating from$2$to $x$ you'll need to know the initial condition of $W(2)$.
  $W(x) - W(2)=\frac{1}{2}x^2 -2$.