A little late to reply but why would you have an expectation that an ADHD child would not be intelligent? There is no link with IQ and ADHD whatsoever, many children/adults with ADHD are highly intelligent and successful. ADHD is a problem with interest and stimulation, so his boredom is most definitely a pointer to ADHD. Fidgetting, not sitting still and not listening are also fairly indicative of ADHD too, though obviously a proper diagnosis would determine this.
Having an ADHD diagnosis is not a condemnation of being disordered, nor is it simply about getting medications (though they are pretty safe and effective) but it's about understanding and accepting your child's differences, providing appropriate effective support to someone with this different neurology and helping them to create an "ADHD-friendly" education and life that suits their talents and strengths - rather than to be trying to normalise. Richard Branson, Michael Phelps, Anthony Hopkins and Justin Timberlake are good examples of ADHD adults embracing their talents.
Bad behaviour and anger are NOT indicative of ADHD. However kids and adults with ADHD have more problems in managing and controlling their emotions. In time if the ADHD child is not supported/helped then they may develop behavioural issues such as Conduct Disorder or Oppositional Defiance Disorder but this only happens for some.
Many children, particularly girls, are not identified as being ADHD because of the mistaken assumptions that ADHD children are disruptive and hyperactive when the vast majority of kids with ADHD are neither. The issues with ADHD are being less stimulated, so more easily bored and distracted, less emotionally controlled, poor time sense (tend to be late, fail to plan and think ahead, procrastination), more maverick (a little less socially compliant, more likely to challenge authority - often for good reason!), and usually more creative, intuitive, empathetic and able to see the big picture.
If your child is ADHD/ADD the odds are likely that at least one parent is too as ADHD is as genetically inherited as height, so it might be a chance for one of you to get some help too.
Here's a link to a short film I made recently about ADHD and the differences that come with it. I really don't know whether you child is ADHD or not but do think it is worth serious research and a positive attitude that is they are indeed ADHD then the best option is to confirm they are and then make appropriate choices as how to best help them and that doesn't have to be medication.
Film on Integrated Model of ADHD
Hope that helps
Andrew Lewis (ADHD myself, diagnosed at 42)
Adult ADHD Coach
www.SimplyWellbeing.com