Exception thrown by a catch{} Block

So there is a problem. The close() method inside the catch{} block throws an IOException which is not caught.

// Loop with problems

try
{
  while ( true )
    sum += instr.readInt();
}

catch ( EOFException eof )
{
  System.out.println( "The sum is: " + sum );
  instr.close(); <—— throws IOException 
}

catch ( IOException eof ) <—— this  catch is for the try{} block 
{                              not for the previous catch{} block
  System.out.println( "Problem reading input" );
  instr.close(); <—— throws IOException 
}

There are various ways to deal with this. One possibility is not to catch the exception that close() throws. Then the method header must be

public static void main(String[] args) throws IOException