a. (i) State the property of definite integrals that relates the integral of a continuous function over two adjacent sub-intervals to the integral over the whole interval.
b. (ii) Prove that for any continuous function f on [a,c] and for any point b satisfying a<b<c, the equality ∫abf(x)dx+∫bcf(x)dx=∫acf(x)dx holds.
c. (iii) Let f(x)=x2 and take a=1, b=2, c=4. Verify numerically that the equality in part (ii) is satisfied for these choices.