R: Create new dataframe with intervals of 2 columns from another dataframe

Question

I have a dataframe, each row consisting of a range stored in 2 columns (int1, int2).

> df <- data.frame(name=c('a','b','c'), int1=c(1,3,7), int2=c(4,8,9))

  name int1 int2
1    a    1    4
2    b    3    8
3    c    7    9

How do I create a new dataframe, with the intervals of each row between int1 and int2 so that I will get:

   name value
1     a    1  
2     a    2
3     a    3
4     a    4 
5     b    3   
6     b    4
7     b    5
8     b    6
9     b    7
10    b    8
11    c    7
12    c    8
13    c    9