Question: Evaluate the following definite integrals:

(a) \(\int\limits_{0}^{1}{{{t}^{2}}dt}\)

(b) \(\int\limits_{-1}^{1}{\left( 2{{y}^{2}}-1 \right)dy}\)

(c) \(\int\limits_{1}^{4}{\sqrt{x}dx}\)

(d) \(\int\limits_{1}^{2}{{{\left( 3x-1 \right)}^{2}}dx}\)

(e) \(\int\limits_{-2}^{-1}{\frac{1}{{{p}^{2}}}dp}\)

(f) \(\int\limits_{2}^{3}{v\left( v-2 \right)\left( v+1 \right)dv}\)