Prerequisites :
#(1):int_a^bphi(x)dx=int_a^cphi(x)dx+int_c^bphi(x)dx; altcltb#.
#(2):int_a^bphi(x)dx=-int_b^aphi(x)dx; altb#.
Given that, #int_0^3f(x)dx=6#,
#rArr int_0^2f(x)dx+int_2^3f(x)dx=6.........................[because, (1)]#.
#rArr 5+int_2^3f(x)dx=6..................................[because," Given]"#.
#rArr int_2^3f(x)dx=1," or, by (2), "int_3^2f(x)dx=-1.......(ast)#.
Now, #int_3^2(f(x)-k)dx=5k#,
#rArrint_3^2f(x)dx-int_3^2kdx=5k#,
#rArr -1-kint_3^2dx=5k...[because, (ast)]#,
#rArr -1-k[x]_3^2=5k#,
#rArr -1-k[2-3]=5k#,
#rArr -1-k(-1)=5k#,
#rArr -1=5k-k=4k#.
#:. k=-1/4#.