Kindly solve all $3$ questions for real analysis $2...$ Define the Riemann Integral $($Definition $7\mathrm{.}1\mathrm{.}1).$

State the Squeeze Theorem $($Theorem $7\mathrm{.}2\mathrm{.}3)$ and give a partial proof in one direction $(lArr).$

Apply the Substitution Theorem to evaluate the following integrals.

$($a$){\displaystyle \underset{1}{\overset{3}{}}}\frac{x^2+1}{\sqrt[\phantom{2}]{x^3+3x}}dx$

$($b$){\displaystyle \underset{0}{\overset{1}{}}}{x}^{2}si{n}^2(x^3)cos(x^3)dx$