(i) Variation of acceleration (a), velocity (v) and displacement (x) with respect to time for different types of motion.
(ii) Displacement calculation from Velocity - Time Graphs: The displacement during an interval between time ti and tf is the area bounded by the the two vertical lines and velocity curve t = ti and t = tf, as given in figures (a) and (b).
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(a) For every part of motion, the velocity is fixed. The displacement Δxi during the i th sub interval is the area vi Δti. So the covered displacement is Δx 
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(b) When v vs. t graph is a smooth complex curve. Area covered by the curve and time axis between t=ti and t=tf is the displacement. The area under the graph may be calculated by using integration.
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(iii) Velocity calculation from Acceleration - time Graphs: shows an acceleration-versus-time graph, the change in velocity between t = ti and t = tf is the area covered by the vertical lines t = ti and t = tf and the acceleration curve
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(a) When the area under the a vs t is a simple curve then the change in velocity v=a0Δt
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(b) When a vs t graph is a complex curve, the area covered the curve may be obtained by using integration
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