Complex line integral

range	$\mathcal{L}$ … continuously differentiable finite lines
definiendum	$\int: \mathcal{L}\to(\mathbb C\to \mathbb C)\to \mathbb K$
range	$L\in \mathcal{L}$
range	$\gamma: [a,b]\to L$ … parametrization
definiendum	$\int_L\ f(z)\,\mathrm dz:=\int_L\ f\left(\gamma(t)\right)\cdot \gamma'(t)\, \mathrm dt$

todo: Continuously differentiable finite lines

If $f$ is holomorphic and two curves $L_1,L_2$ can be deformed into each other, then

$\int_{L_1} f(z)\,\mathrm dz=\int_{L_2} f(z)\,\mathrm dz$

$\int_L f'(z)\,\mathrm dz=f(b)-f(a)$