JEE Math Practice Question

Let g(x) = $$\int_0^x {f(t)dt} $$, where f is continuous function in [ 0, 3 ] such that $${1 \over 3}$$ $$ \le $$ f(t) $$ \le $$ 1 for all t$$\in$$ [0, 1] and 0 $$ \le $$ f(t) $$ \le $$ $${1 \over 2}$$ for all t$$\in$$ (1, 3]. The largest possible interval in which g(3) lies is :

1. A.$$\left[ { - 1, - {1 \over 2}} \right]$$
2. B.$$\left[ { - {3 \over 2}, - 1} \right]$$
3. C.[1, 3]
4. D.$$\left[ {{1 \over 3},2} \right]$$