Hello (sorry for bad usage of English)

i have some issue with this (got to much rusty on this). I need to proof that:

(I try to do it like this... so if I'm wrong or there's "smarter" way to do it i would be very grateful... perhaps i go way back to show what integral is... don't now... please help )

well...

Let the complex functionis defined in regionand let thebe smooth oriented curve with starting point A and end point B. We make division like so:

and make than even finer division:

where (k = 1,2,3,...,n)

where pointis point between pointsand

we form integral sum for division

so we pot this all back in integral sum... and have:

than we have definition...

"For complex number I we say it's Riemman's integral of the complex function f(z) on curve l from point A to point B if and only if :

for

if I exists than we can write...

or

so if this exists than if we have some complex function g(z) = c f(z) where c is constant than we can say that :

and since c is constant than c can come in front of sum and limit so ....

and we can say that we can write

I think this is way to simple to write this much (if it's true)... but I don't know and that's why i need help...

and one more thing... how to proof that :

where A is constant, but without using Newton-Leibniz formula ?!

(it all seems to be trivial until i got start... or I'm just complicating it for myself )

Thanks for any help