Let me know if this code sample puts you on the right track.

XAML

<UserControl x:Class="SL_xamWebChart.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
             xmlns:igChart="clr-namespace:Infragistics.Silverlight.Chart;assembly=InfragisticsSL4.Controls.Charts.XamWebChart.v10.3"
             xmlns:sdk="http://schemas.microsoft.com/winfx/2006/xaml/presentation/sdk"
    mc:Ignorable="d"
    d:DesignHeight="300" d:DesignWidth="400">

    <Grid x:Name="LayoutRoot" Background="White">
        <Grid.RowDefinitions>
            <RowDefinition Height="200"/>
            <RowDefinition />
        </Grid.RowDefinitions>
        
        <StackPanel Grid.Row="0">
            <TextBlock Text="Start Date" HorizontalAlignment="Center" />
            <sdk:DatePicker Name="datePicker1" Grid.Row="1" Height="30" Width="100" />
            <TextBlock Text="End Date" HorizontalAlignment="Center" />
            <sdk:DatePicker Name="datePicker2" Grid.Row="1" Height="30" Width="100" />
            <Button Content="Show Chart!" HorizontalAlignment="Center" Click="Button_Click"/>
        </StackPanel>
        
        <igChart:XamWebChart Grid.Row="1" Name="chart1" Height="200" Width="300" VerticalAlignment="Top">
            <igChart:XamWebChart.Series>
                <igChart:Series ChartType="Pie">
                    <igChart:Series.DataPoints>
                        <igChart:DataPoint Value="10" />
                        <igChart:DataPoint Value="30" />
                        <igChart:DataPoint Value="20" />
                        <igChart:DataPoint Value="40" />
                    </igChart:Series.DataPoints>
                </igChart:Series>
            </igChart:XamWebChart.Series>
        </igChart:XamWebChart>
    </Grid>
    
</UserControl>

Code-behind

private void Button_Click(object sender, RoutedEventArgs e)
        {
            DateTime? t1 = this.datePicker1.SelectedDate;
            DateTime? t2 = this.datePicker2.SelectedDate;
            if (t1 != null && t2 != null)
            {
                Series s = GetDataForTimeRange(t1.Value, t2.Value);
                this.chart1.Series.Clear();
                this.chart1.Series.Add(s);
            }
        }

        private Series GetDataForTimeRange(DateTime t1, DateTime t2)
        {
            // re-write this method to get the appropriate data
            Series series = new Series();
            series.ChartType = ChartType.Pie;
            series.DataPoints.Add(new DataPoint() { Value = 10 });
            series.DataPoints.Add(new DataPoint() { Value = 20 });
            series.DataPoints.Add(new DataPoint() { Value = 30 });
            return series;
        }