How can I evaluate: $$\lim_{h \to 0} \int_{-1}^{1}\frac{h}{h^2+x^2}~dx$$
How I proceed: $$\lim_{h \to 0} \int_{-1}^{1}\frac{h}{h^2+x^2}~dx=2\lim_{h \to 0} \frac{1}{h}\int_{0}^{1}\frac{1}{1+(\frac{x}{h})^2}~dx=2\lim_{h \to 0}\frac{1}{h}\arctan\frac{1}{h}$$ Then how can I prooceed. Please help. Thank in advance.