Consider the polynomial function f(x)=x3−6x2+9x defined on the interval [0,5].
a. (i) Factorise f(x) completely and hence find all its zeros that lie in the interval [0,5].
b. (ii) Using the sign of f(x) on each sub-interval determined by the zeros, identify on which portions of [0,5] the graph of f(x) lies above the x-axis and on which portions it lies below the x-axis.
c. (iii) Hence calculate the total area enclosed between the curve y=f(x) and the x-axis from x=0 to x=5.