For a complex valued function $\displaystyle f(z) $, could someone explain why $\displaystyle \left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|dz $?

Shouldn't it be $\displaystyle \left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|\cdot |dz| $?