i) The Fundamental Theorem of Calculus (part 2): Suppose f is continuous on [a, b], then
∫abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.
ii) Separate out the integration and then use antiderivative of each term:
Rewrite the integration by expanding the cubic term
By separating the integration
∫011dr+∫013r dr+∫013r2dr+∫01r3 dr
By using the antiderivative of each term,
By substituting limits