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I had this integral on my final exam and I was wondering at what point in the interval is the improper integral discontinuous?

[tex]\displaystyle\int^{\pi/2}_{0} \frac{cos(x)dx}{sin^{2}(x) - 3sin(x) -4}[/tex]

I know this is solved by partial fraction decomposition, but I don't see how the integral is improper?

[tex]\displaystyle\int^{\pi/2}_{0} \frac{cos(x)dx}{sin^{2}(x) - 3sin(x) -4}[/tex]

I know this is solved by partial fraction decomposition, but I don't see how the integral is improper?

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