for question 4
we are trying to find
as we know f(x+3) is basically f(x) shifted 3 units to the left, hence we can say that
dx=\int^{4}_{-4}f(x+3)dx)
or we can use the substitution u=x+3 to show the same thing
now we can split
dx)
into
using that identity given we can evaluate that
to find
dx)
we have to use the fact that f(x) is odd, which means that
dx=-\int^{1}_{0}f(x)dx)
you can also get this result by using the substitution u=-x
thus
therefore
dx=6272-2=6270)