\(v = \alpha t + \beta t ^2\)
\(\because v= \frac{dx}{dt}\)
\(\frac{dx}{dt}= \alpha t + \beta t ^2\)
\(\int dx = \int\limits_1^2 (\alpha t + \beta t^2)dt\)
\(= \left[\frac{\alpha t^2}2+\frac{\beta^3}3\right]_1^2\)
\(= \left[2\alpha + \frac {8\beta}3 - \frac \alpha 2 - \frac\beta 3\right]\)
\(x = \left[ \frac{3\alpha}2 + \frac{7\beta}3\right]\)