There may be more than one answer please explain each statement

6) Consider the function f (20 ) = 1 1 if x E [0, 1] and x 7 2 Which of the following statements are true? a) f is integrable on [0, 1] and So f(t) dt = 1. b) If H(x) = fo f(t) dt, then H is discontinuous at x = , because f is not continuous at x = 2. c) If H(x) = fo f(t)dt, then H is continuous on [0, 1) but is not differentiable at x = = because f is not continuous at x = ? d) If H(x) = fo f(t) dt, then H is differentiable at x = = with H'(;) = 2. e) If H(x) = fo f(t) dt, then H is differentiable at x = - with H'() = 1