$\boxed{ \int_{\mathcal S} \left( \nabla \times {\bf A} \right) \cdot d{\bf s} = \oint_{\mathcal C} {\bf A}\cdot d{\bf l} }$
where $$\mathcal{S}$$ is the open surface bounded by the closed path $$\mathcal{C}$$. The direction of the surface normal $$d{\bf s}=\hat{\bf n}ds$$ is related to the direction of integration along $${\mathcal C}$$ by the right-hand rule, illustrated in Figure $$\PageIndex{1}$$. In this case, the right-hand rule states that the correct normal is the one that points through the surface in the same direction as the fingers of the right hand when the thumb of your right hand is aligned along $${\mathcal C}$$ in the direction of integration.
Figure $$\PageIndex{1}$$: The relative orientations of the direction of integration C and surface normal nˆ in Stokes’ Theorem. Image used with permission (CC BY SA 3.0; Cronholm144).