# Complex Integration

For a complex valued function $f(z)$, could someone explain why $\left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|dz$?
Shouldn't it be $\left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|\cdot |dz|$?