YII CGridView with CActiveDataProvider customer limit and offset params

It is a CGridView example with CActiveDataProvider class:

<?php 
$this->widget('zii.widgets.grid.CGridView', array(
    'dataProvider'=>$model->search(),
    'filter'=>$model,
    "itemsCssClass" => "table_design_1",
    "htmlOptions" => array(
        "class" => "div_design_1"
    ),
    'columns'=>array(
        array(
            'name'=>'family_name', 
            'header'=>'First name',
            'type' => 'raw',
            'value' => 'CHtml::link($data->family_name,$data->id)'
        ),
        array(
            'name'=>'given_name', 
            'header'=>'Last name',
            'type' => 'raw',
            'value' => 'CHtml::link($data->given_name,$data->id)'
        ),
        array(
            'class'=>'CButtonColumn',
            'viewButtonUrl'=>'Yii::app()->request->getBaseUrl(true)."/contact/view/".$data["id"]',
            'updateButtonUrl'=>'Yii::app()->controller->createUrl("update",$data->primaryKey)',
            'deleteButtonUrl'=>'Yii::app()->controller->createUrl("delete",$data->primaryKey)',
            "htmlOptions" => array(
                'style'=>'width: 60px;'
            )
        )
    )
)); ?> 

If you need to get total items count find by CDbCriteria you need to write:

$model->search()->getTotalItemCount(); 

But if you want to customize your data provider with custom limit and offset params then you need
to set 'offset' and 'limit' option to 'CDbCriteria' class as following and need to set pagination to false:

$criteria=new CDbCriteria;
$criteria->order = $this->sortString;
$criteria->offset = 5;
$criteria->limit = 10;

return new CActiveDataProvider($this, array(
    'criteria'=>$criteria,
    "pagination" => false
));