Using Apply() and If() statement to sum() two columns

I have a dataframe with 2 columns and I want to use a if/else condition when using the apply function to sum() the rows in each column - specifically, for all the rows where Col1 >= Col2 take the sum() of Col1 and store it in variable a, and for all the rows where Col1 < Col2 take the sum() of Col1 and store it in variable b.

For example

df<-data.frame(Col1=c(1,2,3,4,5),Col2=c(5,4,3,2,1)
df
Col1 Col2
   1    5
   2    4
   3    3
   4    2
   5    1

There are three instances in which Col1 >= Col2, so in Col1 I take the sum() of 3+4+5, which is 12. There are two instances in which Col1 < Col2, so in Col1 I take the sum() of 1+2, which is 3. So

>a
12

>b
3