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Fundamental Theorem of calculus & Estimation Theorem

Hi Guys

Can you help with the attached problem? I think for part (i) and (ii) the answer is the same - i have this as 0 in both cases. However, i'm having problems with part (a) (iii). How do i prove that its not an entire function. Has this got anything to do with the Grid Path Theorem?

For part (b) i have an answer of (3pi/26)(9+e^6). For some reason, this looks incorrect. Can someone work through the problem and tell me if this is what they also get?

For part (c) (i) I get a final answer of -e^3 + e^-3. Is this right and if so does it simplify into a trigonometric function?

For part (c) (ii) I get a final answer of 0. I have done the following for this:

f(z)=zcosh(z^2) = 0.5(2z)cosh(z^2). Hence a primitive of f is f(z) = 0.5sinh(z^2) and the values of 3 and -3 are input into this and subtracted from each other to give 0. Is this correct?