Basic Principles:
#1. The bending moment caused by all forces to the left or to the right of any section is equal to the respective algebraic sum of the bending moments at that section caused by each load acting separately.
#2. The moment of a load about a specified axis is always defined by the equation of a spandrel y = kx^n where n is the degree of power of x.

Area Moment Method:
Part 1:    • Area Moment Method Part 1  Basic Con...  
Part 2: This Video

Related Links:
Moment Diagram by Parts: http://mathalino.com/node/749
Simple Beam Example: http://mathalino.com/node/861
Cantilever Beam Example: https://www.mathalino.com/node/768