I wrongly thought that Sum will be reimplemented to follow the Karr's convention, i.e Sum(i, (i, a, b)) will be    
   ___      
   ╲        
    ╲     i
    ╱       
   ╱        
   ‾‾‾      
a <= i < b   

rather than,
 ___      
   ╲        
    ╲     i
    ╱       
   ╱        
   ‾‾‾      
a <= i < b + 1

and I also assumed that a < b. I think I was confusing Karr's convention and Sigma summation. I think you are correct. I'll make the changes.