Fourier Analysis 1.1 - Problem

Suppose that $\lambda > 0, \phi \in C^1([a, b])$ with $\left| \phi'(x) \right| \geq 1$ and $\phi'(x)$ is monotonic. Then

(1) prove that $$\left| \int_{a}^{b} e^{i\lambda\phi(x)} \textit{dx} \ \right| \leq \frac{2}{\lambda}.
$$(2) Can we extend the above result to the case of multiple integral?