Squeeze theorem for line integrals

Question

For Riemann integrals, it holds that, if $f(x)\leq g(x)\leq h(x)$ for all $x\in[a,b]$ and $\int_a^b f(x)dx=\int_a^b h(x)dx$, then $g$ is Riemann integrable and $\int_a^b g(x)dx=\int_a^b f(x)dx$. Does the same apply for line integrals, i.e. if there is a piecewise smooth curve $AB$ and functions $f,g,h$ such that $f(x,y)\leq g(x,y)\leq h(x,y)$ for all $(x,y)\in AB$ and $\int_{AB} f(x,y)dx=\int_{AB}h(x,y)dx$, then $\int_{AB}g(x,y)dx=\int_{AB}f(x,y)dx$?