f(x+f(y))=f(x)+y, x,y belongs to R.

f(0)=1

then

integral f(10-x)dxbetween limits 0 and 10 is

1. 10
2. 1
3. 10* integralf(x)dx between limits 0 and 1
4. integralf(x)dx between limits 0 and 1

f(x+f(y)) = f(x) +y put y=0 we h ave f(1+x) = f(x) => ?f(1+x)dx = ?f(x)dx Let [F(x)]a to b is ?f(x)dx (on limits a to b) Then [F(1+x)] (on limits a to b) = [F(x)] ( on limits a to b)............ ?f(10-x)dx ( on the limits 0 and 10) = ?f(x) dx ( on the limits 0 and 10) =?f(x)dx ( on limits 0 and 1) +?f(x)dx (on limits 1 and 2) +............ = [F(1)- F(0)] + [F(2) - F(1)] = .............. from (1) we have [F(1 )-F(0)] = F(2) - F(1) =............. = 10* [F(1)-F(0)] = 10*?f(x) dx ( on interval 0 to 1)