Let f: R → R and g: R → R be defined as f(x)={ x+ a, x<0; |x-1|, x ≥ 0 and g(x)= {x+1, x<0; (x-1)^2+ b, x ≥ 0}. where a, b are non-negative real…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ and $\displaystyle g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $$f(x)=\left\{\begin{array}{cl} x+\mathrm{a}, & x<0 \\ |x-1|, & x \geqslant 0 \end{array} \text { and } g(x)=\left\{\begin{array}{cl} x+1, & x<0 \\ (x-1)^2+\mathrm{b}, & x \geqslant 0 \end{array}\right.\right. $$ where $\displaystyle \mathrm{a}, \mathrm{b}$ are non-negative real numbers. If $\displaystyle (g \circ f)(x)$ is continuous for all $\displaystyle x \in \mathbf{R}$, then $\displaystyle \mathrm{a}+\mathrm{b}$ is equal to \_\_\_\_.