First, you use the pipe %>% incorrectly. That is the main problem.
Second, it is better to use mutate once instead of four times.
Also not sure why do you use as integer, but this is a solution for you.
Com %>% mutate(precipitation=as.integer(prcp),
               averagetemperature=as.integer(avtemp),
               populationsize=as.integer(size),
               numberoflymediseasecases=as.integer(cases)) 
Output
 prcp avtemp  size cases precipitation averagetemperature populationsize numberoflymediseasecases
 <dbl>  <dbl> <dbl> <dbl>         <int>              <int>          <int>                    <int>
1    40     30     2   100            40                 30              2                      100
2    50     32     3   200            50                 32              3                      200
3    60     21     4   300            60                 21              4                      300
4    70      2     5   400            70                  2              5                      400
5    80     30     6   500            80                 30              6                      500
If you do not want duplicate columns, select only new ones:
Com %>% mutate(precipitation=as.integer(prcp),
               averagetemperature=as.integer(avtemp),
               populationsize=as.integer(size),
               numberoflymediseasecases=as.integer(cases)) %>%
        select(precipitation, averagetemperature, 
               populationsize, numberoflymediseasecases)
Output
  precipitation averagetemperature populationsize numberoflymediseasecases
      <int>              <int>          <int>                    <int>
1            40                 30              2                      100
2            50                 32              3                      200
3            60                 21              4                      300
4            70                  2              5                      400
5            80                 30              6                      500
If you can mutate columns and assign a specific column type, using 
Changing column types with dplyr
If you specify exactly what are you trying to do, I will try to help additionally.