Mathematics

Problem

Let

h(x)=x^{2}+2mx+(m^{2}-1)

, where

m

is a real parameter. The function is considered on the interval

[m, m+2]

. (i) Express the average value of

h(x)

[m,m+2]

in terms of

m

. (ii) Determine all real values of

m

for which the average value obtained in part (i) equals

3