Bombay plague epidemic problem (improper integrals)

[chrisbush.sax]

Here's the question:
The death rate of the plague is
R=890sech^2(.2t-3.4)
R is deaths/wk and t is time in weeks since plague began.
(a) What is the peak death rate and when did it occur.
--I took the derivative and set equal to zero and found the answer to be 890 deaths/wk at t=17

(b) Estimate the total deaths with definite integral from -infinity to infinity of R(t)
--Found the limit to be 8900 total deaths by splitting into 2 improper integrals and taking the limit as the bounds go to +/- infinity, etc.

(c) Show that more than 99% of deaths occurred in the 1st 34 weeks.
--found definite integral from 0 to 34 of R(t) to be 8880 which is approx. 99.8% of 8900

(d) Find a model for R in the form a/(t^2-2bt+c) where c>b^2. New model (N) has same peak death rate at the same time as the original model, and the definite integral from -infinity to infinity of N is the same as the original model.
--I found the integral of N to be pi(a/sqrt(c-b^2))
Setting this equal to 8900 gives me:
8900=pi(a/sqrt(c-b^2)

--I took the derivative of N and it is:
-a(2t-2b)/(t^2-2bt+c)^2
N'(17)=0=-a(34-2b)/(289-34b+c)^2
...gives me b=17
...and a=0
...and c=289
...which makes no sense.

Please help! I am getting depressed thinking about death rates all the time!