Let f : R R be defined as
f(x) = \left[ {\matrix{
{[{e^x}],} & {x < 0} \cr
{a{e^x} + [x - 1],} & {0 \le x < 1} \cr
{b + [\sin (\pi x)],} & {1 \le x < 2} \cr
{[{e^{ - x}}] - c,} & {x \ge 2} \cr
} } \right.
where a, b, c R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?