This is a Real Analysis Question. Please Prove or Disprove

Given a function f on an interval [a, b] and a partition P of [a, b], we define the left-endpoint sum for f and P by n EL(f, P) = >f(tk-1) (th - tk-1). k=1Suppose f is a function on [0,1] with the following property: there is a number 3 E R such that for any 5 > 0, we can nd 6 > 0 so that for any partition P of [0,1] with mesh(P)