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[tex]\int \frac{1}{x ^ 2}dx = - \frac{1}{x} + C[/tex]

Let [tex]f(x) := \frac{1}{x ^ 2}[/tex]

[tex]f(x) > 0, \forall x \in \mathbb{R}[/tex]

[tex]\int_{-1}^{1}f(x)dx = -1 - (-(-1)) = -2[/tex]

Why this happened??? It's obvious that [tex]f(x) > 0, \forall x \in \mathbb{R}[/tex] and -1 < 1, but why [tex]\int_{-1}^{1}f(x)dx < 0[/tex]

I think it should be : [tex]\int_{-1}^{1}f(x)dx = + \infty[/tex]

What have I done wrong????

Viet Dao,