Show these statements are true for continuous function f, but false for Riemann integrable functions f.

1. If f:[a,b] --> R is such that f(t)>=0 for all t in [a,b] and

integral( f(t), a, b) =0 then f(t)=0 for all t in [a,b]

2. integral(f(x), a, t) is differentiable and the derivative = f(t)