[R] From vector to a step function

[Alaios]

Greetings R members.

I have a few vectors that denote the 'steps' of different step functions
v1=c(3,4,5,1,2,3,4,5)
v2=c(5,6,2,4,7,3,2,5)
v3=c(1,2,4,7,3,1,3,5)

Here v1,v2,v3 are considered as the steps for the f1,f2,f3 step functions.

For example f1 looks like that (step size is always same and fixed)

f1= 3 (x>=-3,x<-2)
f1= 4 (x>=-2,x<-1)
f1= 5 (x>=-1,x<0)
f1= 1 (x>=0, x<1)
and so on.

What I only have are these vectors that are interpreted as functions (as shown above, x (step is 1 here). I would like to ask your help of how I can create some function that reads one of the vector v1,v2,v3.... and returns results that are acceptable by integrate() function.

Usually integrate wants a pre-defined function like
myfunc(x)<-function{ x^2 }
but this is not the case here.

Could you please give me some hints how I can proceed?

I would like to thank u in advance for your help

Regards
Alex