How is the lower sum of refinement partition greater than the lower sum of the partition of [a,b]? let f be abounded function on [a,b].If P$\subset$Q , then
L(f, P)$\leq$ L(f,Q)
I know when we do refinement of partition our answer of the area under curve becomes more precise to the actual value. But I am not able to construct the rigorous for the same.
let P be a partition of the closed interval [a,b],given by
P=$\{a=x_0,x_1,\ldots,x_n=b\}$ let Q be refinement of partition P with one more point u , such that
Q=$\{a=x_0,x_1,\ldots,x_i,u,x_{i+1},x_n=b\}$
and i don't know how to proceed further.