## University Calculus: Early Transcendentals (3rd Edition)

$\int_{-\pi/4}^{0} sec(x) dx$.
By using the definition of the definite integral, P is a partition of $[-\pi/4,0]$, therefore the lower and upper limits of the integration are -$\pi/4$ and $0$. $f(c_{k})=sec ({c_{k}})$ is the function in the additive of the Riemann sums, therefore $f(x)=sec(x)$. Therefore the solution is: $\int_{-\pi/4}^{0} sec(x) dx$.