Integral Problem help Given definite integral 
$
f(t)=\int_{0}^{t} \frac{x^2+13x+36}{1+{\cos{x}}^{2}} dx
$    
At what value of $t$ does the local max of $f(t)$ occur?
What I did is replace $x$ variable with $t$...
and the $f'(t)=\frac{x^2+13x+36}{1+{\cos{x}}^{2}}=0$
because looking for local extrema points is when the derivative is $0$.
So based on my knowledge, $t = -4$ and $-9$ when $f'(x)=0$
and used a point before $-4$, between $-4$,$-9$ and after $-9$
and pug it back in the $f(t)$.
Did I do it right?
Thanks

Note that the first derivative is positive up to $-9$, then negative up to $-4$, then positive. So there is a local max at $-9$ and a local min at $-4$.  
I do not know of any way of evaluating the function at the local max and local min except numerically, say using Simpson's Rule.
