Without solving the integral prove that:
(a) $\int_1^3 \frac{dx}{x^2+6} \leq \int_1^3 \frac{dx}{x+4}$
(b) $\int_0^1 x \, dx \geq \int_0^1 x^2 \, dx$
(c) $\int_2^6 \frac{x}{x+8} \, dx \leq \int_2^6 \frac{x}{10} \, dx$
(d) $\int_1^2 x \, dx \leq \int_1^2 x^2 \, dx$
