Let `f:[a,b]rarr[1,infty)` be a continuous function and lt `g: RrarrR` be defined as `g(x)={(0, "if x" lt a),(int_a^x f(t)dt, "if a"lexleb),(int_a^b f(t)dt, "if x"gtb):}` Then
a) `g(x)` is continuous but not differentiable at `a`
b) `g(x)` is differentiable on `R`
c) `g(x)` is continuous but nut differentiable at `b`
d) `g(x)` is continuous and differentiable at either `a` or `b` but not both.