Statics Engineering Problem Involving Beams

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Is your solution incorrect? Is there a bending moment the the left of R1?
 
I am not a civil engineer but I read that the bending moment is the integral of the sheer force diagram. It looks like this is what you have done. I see there is a bending moment to the left of R1 due to the loading of the beam.
 
I checked your numbers up to M3 and I think you are doing good.