JEE Math Practice Question

Given : $$f(x) = \left\{ {\begin{matrix} {x\,\,\,\,\,,} & {0 \le x < {1 \over 2}} \\ {{1 \over 2}\,\,\,\,,} & {x = {1 \over 2}} \\ {1 - x\,\,\,,} & {{1 \over 2} < x \le 1} \\ \end{matrix} } \right.$$ and $$g(x) = \left( {x - {1 \over 2}} \right)^2,x \in R$$ Then the area (in sq. units) of the region bounded by the curves, y = ƒ(x) and y = g(x) between the lines, 2x = 1 and 2x = $$\sqrt 3 $$, is :

1. A.$${1 \over 2} + {{\sqrt 3 } \over 4}$$
2. B.$${1 \over 2} - {{\sqrt 3 } \over 4}$$
3. C.$${1 \over 3} + {{\sqrt 3 } \over 4}$$
4. D.$${{\sqrt 3 } \over 4} - {1 \over 3}$$