Let a function \( f: R \rightarrow R \) be defined as \(f(x)=\left\{\begin{array}{ccc}\sin x-e^{x} & , \quad \text {…

Let a function \( f: R \rightarrow R \) be defined as

\(f(x)=\left\{\begin{array}{ccc}\sin x-e^{x} & , \quad \text { if } x \leq 0 \\a+[-x], & \text { if } 0<x<1 \\2 x-b, & \text { if } x \geq 1\end{array}\right.\)

where \( [x] \) is the greatest integer less than or equal to \( x \). If \( f \) is continuous on \( R \), then \( (a+b) \) is equal to

[JEE Main 2021, 20 Jul (Shift 1)]