I am reading Morita's book The Geometry of Differential Forms and am confused about a statement made on page 62, which is in section 2.1 c).
He says:
"Then obviously
$$dx_i(\frac{\partial}{\partial{x_j}}) = \delta_{ij}$$
From another point of view, since $\frac{\partial}{\partial{x_j}}$ is a unit tangent vector in the dierection of $x_j$, we can consider that [the above fact] reflects the fact that if we integrate the constant function 1 with respect to $x_i$ from 0 to 1 along the $x_j$ - axis, the value is $\delta_{ij}$."
Can anyone explain how this reflects that fact about integrating the constant function? I don't see the connection.