integral - C++ Integration Solution using Riemann Sum : Loses validity for greater than 10 partitions -

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In an attempt to give a concise solution to an approximation of integral using the sum of Riemann, I ran into a strange problem Gone: If the user requested a partition number of more than 10, the program failed any idea? Here's the code: 

  // Integral #include & lt; Algorithm & gt; # Include & lt; Iomanip & gt; # Include & lt; IOS & gt; # Include & lt; Iostream & gt; # Include & lt; Stdexcept & gt; # Include & lt; Iomanip & gt; Using std :: cin; Using std :: cout; Using the Std :: endl; Int func (int x); Int main () {cout & lt; & Lt; "Please enter the left and right border:"; Int left, right; Cin & gt; & Gt; Left & gt; & Gt; right; Cout & lt; & Lt; "Please enter # (& gt; 0) from the partitions:"; Int r; Cin & gt; & Gt; R; Int width = (right - left) / R; Integer = 0; For (int i = 0; i     
 
 Using partition size greater than 10 is not your actual problem.  
 You are using an integer for your variable and function return value, when you should use  float  or  double . 
 
 For example: 
 
  width = (right - left) / r;  
 
 If  (right - left) & lt;  The width will be zero!

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