Answer to Question #14922 in Calculus for Nick

Question

Justify, with a written explanation or a mathematical reasoning and with a sketch of at least two different cases,

the following properties of integrals:

a) If f(x) is less than or equal to g(x) for a<=x<=b then

integrate from a to b of f(x)dx is less than or equal to integrate from a to b of g(x)dx


b)abs(integrate from a to b of f(x)dx) is less than or equal to integrate from a to b of abs(f(x))dx