Lets say we have two functions f and g that are riemann integrableon the interval [a,b] If (f(x)-q(g(x)))^2 is greater than zero for all real q, is the integral from a to b of (f(x)-q(g(x)))^2 greater than zero? Also, lets say we have a function h(x) that is defined from [0,1] as follows: f(x) is zero if x is not 0.5 and if x is 0.5, then f(x) is a number, lets say 15. What is the integral from a to b of this function? If it is zero, we can continue to add points. When does this process yield a nonzero integral?