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The problem wishes us to integrate [tex]sec^{2}(x)[/tex]
-However, we know based on the derivation of tan (x)
[tex]\frac{d}{dx}tan(x)=sec^{2} (x)[/tex]
Bascially integration is the reversal of the derivation:
Thus
[tex]\int\limits^a_b {sec^{2}(x)} \, dx =tan(x) +C[/tex]
Since there are no bounds, we must add a constant 'C' as we don't know if there was an initial value
Hope that helps!